Chelsea currently sit in third spot, while United are fifth in the Premier League and can close the gap to Leicester if they beat relegation-threatened Villa on the road on Thursday.
The battle for Champions League qualification continues.
Former Leicester City and Chelsea defender Frank Sinclair believes Frank Lampard's Blues and Manchester United will make the top four.
Leicester and Chelsea swapped places on Tuesday after the Foxes played out a 1-1 draw with Arsenal on Tuesday night.
While Chelsea sealed a 3-2 win against Crystal Palace at Selhurst Park to move into the third position in the Premier League table.
United's fine form has brought them closer to Leicester and they are unbeaten in 16 games. If the Red Devils beat Aston Villa on the road on Thursday, they'll go one point behind the Foxes who they visit on the last day of the season.
"Manchester United are in great form at the minute," Sinclair said on BBC Radio 5 Live.
"They don't look like they're going to drop points any time soon and with a win in their next game they'll go right behind Leicester by a point.
"I thought yesterday's game was really important for Chelsea to get the three points. It was sticky towards the end, with a bit of a nervous finish, but they got the job done. I think it was crucial to get their noses in front of Leicester.
"For me, I still fancy Man United will get in the top four and I believe Chelsea will join them."
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