With the heavily sceptical future of current manager Antonio Conte, the London side has begun the process of finding a suitable replacement, with former Barcelona manager, Luis Enrique leading the list.
Conte aimed another dig in the direction of Mourinho and Manchester City manager Pep Guardiola as his team closed on their title triumph.
"Now he's recovering, I think that [Schalke] could be an interesting option for the player, to try to recover with them".
One name not under consideration is Carlo Ancelotti, which is surprising since the 58-year-old won a league and FA Cup double with Chelsea in 2010.
"But I believe that when you go to touch Mourinho, he is very good at any verbal situation".
Conte has grown frustrated with the Chelsea hierarchy over the club's recruitment strategy, particularly during a troubled summer transfer window that saw top targets Romelu Lukaku join rivals Manchester United and Alex Sandro remain at Juventus. This is the history of this club for the manager. But there is something odd when after the first game we lost against Burnley and the press pushed quickly to sack me for another coach. "I didn't think they would get to this point".
Chelsea sensing that Conte won't stay at the club for long have already agreed terms with Massimiliano Allegri, who has enjoyed great success at Juventus.
Conte was unable to provide an update on Eden Hazard's contract, amid suggestions a new deal for the Belgium playmaker is close, saying it was a club matter.
Antonio Conte wasn't the only subject in Mourinho's Man United press conference.
He said: "I must be honest".
Conte's side were held to a frustrating goalless draw in their League Cup semi-final first leg against Arsenal on Wednesday despite creating a host of chances.
Speaking before the visit of Leicester City on Saturday, Conte was pressed on whether he is searching for a striker to add competition for Alvaro Morata and Michy Batshuayi. "He's a great player and knows very well in my first season in Juventus we tried to buy him from Udinese and then he chose to go to Barcelona".