Senate Minority Whip Dick Durbin, D-Illinois, made the remark after he was asked by a reporter whether Biden should consider a presidential bid.
"I can tell you this: I have great respect for Joe Biden, a former colleague in the Senate who served us as vice president. He's an extraordinary person and I count him as a dear friend. He owes it to himself and his family to take a hard look at this; I'll wait to see what he decides to do before I presume whatever his decision will be."
Durbin added that it would be "too soon" to say whether he would support Biden if he decided to run.
Also on Tuesday, former Maryland Gov. Martin O'Malley
said he would "welcome" Biden into the Democratic presidential primary.
"Vice President Biden is a very, very good man," he told CNN during a press gaggle after a roundtable discussion at which he spoke with the black leadership group 20/20 Leaders of America. "I think he cares very passionately about the future of our country and whether or not the American dream is a reality for families or whether we let it turn into a lie."
Though he did not attack her by name, O'Malley made clear reference to frontrunner Hillary Clinton, using a concise and firm tone as he alluded to what many call the Clinton machine.
"People are looking for alternatives. They don't like being told who they're supposed to be voting for and they don't like the sinking sense in the air that somehow big money determines who our nominee is going to be."
Speculation about another potential Biden presidential run intensified over the weekend after a close confident of the late Beau Biden joined the SuperPAC Draft Biden.
Just Monday, former South Carolina Democratic Chairman Dick Harpootlian told CNN that "five major political people in South Carolina" had called him about joining a Draft Biden effort in the Palmetto State. Harpootlian pointed out that two of those people were proclaimed Clinton supporters who would "jump to Biden" if he entered the race.
During the roundtable, the former governor also laid out a plan for a constitutional amendment to protect voting rights, which CNN first reported
This was O'Malley's first visit to South Carolina since he announced his bid for presidency almost two months ago.