Manchester City have indicated that they are ready to walk away from negotiations to sign Arsenal’s Alexis Sánchez as José Mourinho admitted he is interested in adding the Chile forward to his Manchester United squad.

Having come close to signing Sánchez in the summer, City had felt that a deal to secure the arrival of the 29-year-old in the January transfer window was imminent after they agreed personal terms with his representatives over a contract worth £13m a season.

A verbal offer of £20m was lodged last week, with City informing their Arsenal counterparts that they were unwilling to raise their offer despite being informed it would take a £35m bid to make the move happen this month.

However, after United indicated on Thursday that they were willing to offer Sánchez higher wages and pay £25m to bring him to Old Trafford, their neighbours have warned they will not be held to ransom for a player whose contract at the Emirates expires in June. It is understood that the Premier League leaders feel the overall price including transfer fee, wages and agent costs are too high, with City unconcerned that their stance may cause Sánchez to sign for another club in the meantime.

That appears to have opened the door for United, with Mourinho admitting on Friday he would be interested in what he described as a “phenomenal player”.

“At the general level what I can say is myself and Manchester United board, owners, we don’t believe a lot in the January market, we don’t believe in signing a player just to sign a player,” Mourinho said. “What we believe really is there are some players in the football world if you have the chance to sign them in January, March or July, you have to try and that’s it.

“But in relation to Alexis Sánchez I don’t say a word. The only word I can say is he is a phenomenal player, apart from that an Arsenal player and I feel I shouldn’t say much more than this. I don’t think it’s – I don’t know, ethical or correct – to be speaking about players of other clubs. If somebody speaks of one of my players to say they are interested, I wouldn’t be very happy. Sánchez is an Arsenal player. I don’t know but probably this weekend he is going to defend Arsenal colours, so I don’t think it’s correct to say things about Alexis Sánchez.”

City agreed a £60m deal with Arsenal in August, only for the transfer to collapse when Arsène Wenger failed to complete a move for Monaco’s Thomas Lemar on deadline day. Wenger admitted on Friday that he was unsure whether the player signed from Barcelona in 2014 would still be at the club next month but insisted Sánchez would not be allowed to leave unless they secure a replacement.

City had been convinced of Sánchez’s desire to work with Pep Guardiola again and were prepared to wait until the summer to sign him if necessary until a knee injury suffered by Gabriel Jesus on New Year’s Eve appeared to alter their plans. Yet with the Brazil striker now expected to be back in training within three weeks, there is less urgency to add to the squad this month.

Guardiola, whose City side travel to Anfield to face fourth-placed Liverpool on Sunday looking to extend their unbeaten run in the Premier League this season to 23 matches, refused to discuss any move for Sánchez.

“I understand completely this question, I understand you are doing your job, but you know my answer,” he said. “I am not going [to speak about it]. I’m focused on Liverpool, believe me. Alexis – everyone knows how good he is, but I am not going to answer about Alexis or other players.”