The move will happen as soon as possible, the source said.
Earlier, a spokeswoman for the popular tourist destination in Lake Buena Vista, Florida, said officials were reviewing the placement and wording of warning signs.
"We are conducting a swift and thorough review of all of our processes and protocols," Walt Disney World Resort Vice President Jacquee Wahler said in a statement Thursday. "This includes the number, placement and wording of our signage and warnings."
The Graves family was at a movie night outdoors Tuesday night at the Grand Floridian resort when the boy waded into about a foot of water in Seven Seas Lagoon, authorities have said. Witnesses, including the boy's horrified parents, tried to save him as a gator dragged him underwater, witnesses told authorities.
Search crews combed the water for hours before they found the toddler's body.
There are "No Swimming" signs at the lagoon, but there are no warning signs about alligators.
All the beaches at the resorts at Walt Disney World remain closed.
Some had questioned whether signs specifically warning of alligators should have been placed at the luxury property.
"We have a large property, and from time to time, we have to remove alligators from our property," Wahler said "Nearly one-third of Walt Disney World property is set aside as a conservation area and these areas attract a variety of native wildlife."
Hunt for gator
As a family mourns the death of their son, investigators are trying to pinpoint which alligator attacked him.
The gator responsible might be dead -- but authorities aren't sure.
Search teams captured and euthanized at least five alligators as they searched the water for the boy, officials said.
Forensics teams will try to determine whether one of the alligators already taken from the lake is the one that dragged off the boy, officials said. One method will be to compare bite marks to the teeth of the gators.
If not, the search for alligators in the lake will continue.
"We're going to make certain that we have the alligator that was involved, and that we remove it from the lake," Florida Fish and Wildlife Conservation Commission Executive Director Nick Wiley said.
Spokeswoman Tammy Sapp said the investigation was ongoing as of Thursday afternoon.
Disney beaches closed
By midmorning Wednesday, Disney had closed all beaches in its resort area "out of an abundance of caution" after the attack, a Disney representative said.
"Everyone here at the Walt Disney Resort is devastated by this tragic accident," Wahler said in an earlier statement. "Our thoughts are with the family. We are helping the family and doing everything we can to assist law enforcement."
Body found intact
A dive team found the boy's body intact in 6 feet of murky water about 10 to 15 yards from where he was attacked, Orange County Sheriff Jerry Demings said Wednesday.
Lane's body had only a few puncture wounds, according to a source familiar with the investigation.
"Of course, the autopsy has to confirm that, but there is likely no question in my mind that the child was drowned by the alligator," Demings said.
The fact that the body was found intact makes sense, said Jeff Corwin, host of "Ocean Mysteries" on ABC.
"That gator came in, grabbed that boy, pulled him, the dad startled that gator, the gator let him go and then the boy drowned," he speculated.
Alligators don't swim that far -- they sink into the murky water and lurk there -- which may explain why the father did not see the boy when he jumped into the water to try to save him, Corwin said.
A community mourns
The boy's parents, Matt and Melissa Graves of Elkhorn, Nebraska, issued a statement on Thursday.
"Words cannot describe the shock and grief our family is experiencing over the loss of our son. We are devastated and ask for privacy during this extremely difficult time," they said. "To all of the local authorities and staff who worked tirelessly these past 24 hours, we express our deepest gratitude."
As word spread about the toddler's death, friends and neighbors in the family's hometown offered words of condolences and support.
Omaha Infogroup, a business data firm where Matt Graves works, released a statement saying the company was stunned and heartbroken.
"Matt's family is the light of his life and his family's anguish is our own," the statement said, according to CNN affiliate KMTV
. "What happened last night was a terrible accident and one that is devastating to the entirety of Infogroup."
The family's church, St. Patrick's Catholic Church in Elkhorn, posted a message to parishioners on its website
"It is with a heavy heart," the message said, "that we inform you of a tragic loss in one of our parish families. ... Please honor their privacy at this time and keep them in your prayers."
The tragedy has shaken the community, said Norman Hale, principal of Elkhorn St. Patrick's School.
"It's unimaginable, the grief and what they're going through right now," he told CNN affiliate KETV
More than a million gators
In Florida, alligators may be a common sight, but attacks are rare. If a human gets close to alligators, 99% of the time they take off, Corwin said.
As of April, only one other major alligator attack had been reported in the state this year, according to the Florida Fish and Wildlife Conservation Commission. That person survived the attack, but required medical care.
In 2015 there were nine major unprovoked attacks in Florida, with one fatality.
Officials said Disney World has never experienced an incident like the one involving the boy.
There are an estimated 1.3 million alligators in Florida, said Arnold Brunell, a wildlife biologist and researcher for the Florida Fish and Wildlife Conservation Commission. That number has been holding steady for the past five years, he said.
According to the wildlife commission's website, at least 23 people have been killed by Florida alligators since 1973. That includes several children. One was a 4-year-old girl who in 1988 was killed while walking along the edge of a lake in Charlotte County.
Another was 10-year-old Bradley Weidenhamer, whose parents said they can relate to what Lane Graves' parents are going through.
Bradley died when an alligator grabbed him and dragged him into the Loxahatchee River in Martin County on June 20, 1993.
In that 43-year time frame, 373 people were bitten by alligators; 247 required medical care beyond simple first aid.