"I hope (he runs). We're doing everything we can to encourage him to run," McConnell said in an interview on MSNBC's "Morning Joe" while discussing the impact of Donald Trump's candidacy on down-ballot Republican candidates in swing states.
Rubio initially said he didn't want to run for re-election to the Senate, and his dislike for the deliberative body became well known
over the course of his unsuccessful presidential campaign.
But amid growing pressure
from top Republicans, Rubio has left the door open to a run he'd been vocally reluctant to make. He told
CNN's Jake Tapper that "maybe" he'd run for the Senate if his close friend, Florida Lt. Gov. Carlos Lopez-Cantera, was not in the race.
But Lopez-Cantera's campaign has dismissed questions that Rubio would jump in, with spokeswoman Courtney Alexander saying last week that her boss is "focused on winning this Senate seat."
Rep. David Jolly has promised to step aside if Rubio were to jump into the race, saying in a statement that he would "support Rubio for re-election" if he decided to run.
Others, however, have signaled they would stay in the race, including Rep. Ron DeSantis and businessmen Carlos Beruff and Todd Wilcox. And Rubio would undoubtedly face attacks over his immigration record and missed votes
-- and would quickly have to raise millions of dollars -- all challenges he would have to consider if he filed papers before the June 24 deadline.
"Carlos Beruff is staying in this race," said Beruff spokesman Chris Hartline. "As usual, Washington Republicans think they can control the race, but the voters of Florida will decide who our nominee is."
McConnell also said Tuesday that he was unsure of the effect Trump would have atop the Republican ticket on Senate candidates, though he expressed confidence.
"I think we don't know yet (what Trump's effect will be). What I do think is that Senate races are big enough to where you can paint your own picture and all of our candidates are going to be in a good position to run. One of the things that we're working on ... is to draft Marco into running again," McConnell said.
And the Senate majority leader was resolute in his support for Trump.
"My view is Trump has earned the nomination because he went out and got the most votes and we need to be respectful of the process that has produced this nominee," he said.