Ole Gunnar Solskjaer's position at United has been extremely precarious in recent weeks.
There was much speculation about his future at the club following the club's humiliating 5-0 defeat to Liverpool last month.
Solskjaer survived, but speculation has increased once again following their convincing 2-0 loss to Manchester City on Saturday afternoon.
And now Caught Offside are claiming that Rodgers has verbally agreed to replace Solskjaer.
There are still hurdles to overcome before a deal is completed, however.
The report claims United want to hire Rodgers now, but his preference is to wait until the end of the campaign.
Discussions are said to be continuing to try and come to an agreement.
A source close to the deal told CaughtOffside: “Brendan Rodgers to Manchester United…he’s agreed it, there’s just question marks over when he’ll take over. That could be at the end of the season, which he would prefer, but United are pushing for now.”
Rodgers is one of the best managers in the Premier League.
He's had success with Liverpool, Celtic and is now doing a remarkable job at Leicester City.
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He guided The Foxes to an FA Cup triumph and has made them perennial top four contenders.
The report comes just a week after Rodgers outlined his commitment to Leicester.
"I don't even think about it [my future] - and that's the brutal honesty," he said, per Manchester Evening News.
“I’m sure the supporters are probably tired of it. At Leicester, there is always a link.
"My focus is always here with Leicester and developing the football club on to that next level, where you're competing for European football and challenging for honours.
"Everyone here at the club, from the chief executive to the director of football - staff, players - we're all very much on the same path, same vision."