Both sides are in FA Cup action this weekend - City play Barnsley on Saturday then United host Chelsea on Sunday.
Mancini, who watched United crash out of the Champions League with a 3-2 aggregate defeat to Real Madrid on Tuesday, hopes that the Red Devils' cup exertions can derail their season.
"It's possible because when United play Chelsea it's possible that Chelsea will beat United," said the Italian. "It's not impossible in football.
"One or two weeks can change everything. For this reason we should be confident for the Premier League.
"If they are so strong that they will win all their games then okay, but if they lose one or two games or a point then we should be ready to take this opportunity."
City will travel to Old Trafford in the Premier League on Monday, April 8.