Manchester City could walk away from Alexis Sanchez deal
Sanchez has been a long-time target for City but Press Association Sport understands the Premier League leaders feel the overall cost to sign the forward this month - including transfer fee, agent costs and wage demands - is currently too high and must come down.
The 29-year-old is out of contract in the summer and City would hope to do a deal for around £20million, yet it is believed they have been quoted £35milliion.
Pep Guardiola's club are thought to be unconcerned that their stance opens the door for another club to step, even if that team is their cross-city rivals United.
And Mourinho did little to quash any potential move from United when asked about their possible interest in Sanchez.
"I don't think it's correct to say things about Alexis Sanchez," he said.
"At the general level, what I can say is that myself and the Manchester United board, we don't believe a lot in the January market. We don't believe in signing players just to sign a player, just to do something. We don't believe in that.
"What we believe really is that there are some players in the football world, if you have a chance to sign them, it doesn't matter if it is in January, March or July you have to try.
"But in relation to Alexis Sanchez, I don't say a word. The only word I can say is the same word that everybody says, he's a phenomenal player.
"Apart from that, (he's an) Arsenal player, I feel I shouldn't say much more than this."
City, who were unsuccessful with a £60million offer for Sanchez last summer, have been convinced of the forward's desire to work with his ex-Barcelona manager Guardiola again for some time but they were prepared to wait until his contract expires in June.
A knee injury suffered by Gabriel Jesus on New Year's Eve had the potential to change thinking and bring forward a potential deal, but the Brazilian could now be back training within three weeks.
City understand Sanchez is keen to leave in the current transfer window but they will not be pressured into overpaying by the player's representatives, Arsenal or by interest from elsewhere.
Guardiola refused to discuss the matter when speaking prior to Mourinho on Friday.
"I am not going (to speak about it)," he said. "I'm focused on (playing) Liverpool, believe me. Alexis - everyone knows how good he is, but I am not going to answer about Alexis or other players."
Arsenal manager Arsene Wenger, meanwhile, has stressed that Sanchez will only be allowed to leave north London this month if a replacement is found.
The Gunners, who maintain they have not yet received an approach for Sanchez, have been linked with Bordeaux's Brazilian forward Malcom.
Wenger said: "Of course I want a quick resolution.
"Is he (Sanchez) replaceable in the way that we find exactly the same player? Certainly not, but there's always a way to find a different balance.
"Alexis is an exceptional football player, he's a world-class player and if that happens (he leaves) we have to find a different balance in the team."