The Portuguese claimed he had no plans to sell or buy in the January transfer window but did not rule out Germany's Schuerrle exiting Stamford Bridge, while Egypt winger Mohamed Salah has also been linked with a switch.
With both players said to be growing frustrated with a lack of first team opportunities, media reports said Bundesliga side VfL Wolfsburg have made an offer for Schuerrle, while Salah is said to have piqued the interest of Serie A side Roma.
"The principle is that we would like him (Schuerrle) to stay," Mourinho told reporters on Friday ahead of Saturday's FA Cup fourth round game at home Bradford City.
"The question is not whether he is allowed to go or not. The question is not whether we get a good offer. The question is whether we have a phenomenal offer and for the player to be super-keen to accept a new challenge in his career, because we don't want to sell our players."
Mourinho said Salah and Schuerrle would be involved for the FA Cup clash, which heralds the start of a crucial week in Chelsea's season.
A 1-1 draw with Liverpool in the League Cup semi-final first leg has left all to play for in the return encounter at Stamford Bridge on Tuesday, and four days later Premier League champions Manchester City also visit London.
"My team tomorrow reflects the fact that if we lose the game, we are out, and if we draw, we have to go to Bradford," Mourinho said.
"We don't want to be out, and we don't want a second match against Bradford."
(Reporting by Toby Davis; editing by Justin Palmer)
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