Mignolet has enjoyed a five-year spell with Liverpool since joining from Sunderland, but Klopp revealed he would have liked to have played first-team football elsewhere this season.
United have been far from good enough thus far.
The two teams are set to meet again in the Premier League on Saturday and Chelsea assistant manager Gianfranco Zola says the Blues are greedy and want to win both games.
The Croatia worldwide has yet to feature for the Premier League leaders this season having returned from the World Cup with a stomach injury but may be included in Jürgen Klopp's squad for the third round tie at Anfield having resumed full training.
Liverpool are still monitoring Virgil van Dijk's bruised ribs, which forced him off in the second half of Saturday's win over Southampton.
The Spain global has been Chelsea's first choice right winger in the current season and when he is not available, manager Maurizio Sarri prefers the Brazilian, Willian, to deputize for him.More news: How Onyango, Desabre voted in the Fifa Best Men’s Player
However, Liverpool manager Jurgen Klopp has said that the issue is not serious but confirmed that it is still causing the defender some problems as it is painful.
This is the eighth League Cup meeting between Liverpool and Chelsea and the first at the third round stage since November 2000, when the Reds won 2-1 at Anfield with goals from Danny Murphy and Robbie Fowler. Trained completely normal now, four times. It's not that you think the first two-three rounds you go through somehow, and from the semis on it starts getting exciting...
"He trains fantastic and he deserves this game".
Although, the young boy never thought his wish would come to realisation as the PFA player of the year spotted the inscriprion and gave him the shirt.
"It's too much when you play extra-time, and your opponent for the weekend is sat in front of the television and is happy". That is a really good, strong group'.