On Monday, the Manchester Evening News reported that City, long-term suitors of Sanchez, had decided to drop their interest in the Chilean after holding meetings with the club to discuss the financial aspects of the deal.
While City manager Pep Guardiola, who coached Sanchez at Barcelona, was keen to add the forward to his squad, his wage demands and transfer fee were considered excessive by the club given he is out of contract at the end of the season.
Mourinho confirmed that United were interested in Sanchez but said he was "neither confident nor unconfident" about securing his signature.
"I am just relaxed with the feeling that he is an Arsenal player, he can stay there, but also with the feeling that he can move and if he moves I think we have a chance," he told reporters after Monday's 3-0 win over Stoke City at Old Trafford.
"I think most probably a player like him has other big clubs interested. Who knows? I think him, Mr (Arsene) Wenger, Mr (Arsenal CEO Ivan) Gazidis, they are the ones that know really what is going to happen," added Mourinho.Earlier speaking to the BBC, the United manager said: "He is an Arsenal player, if he stays it's great for Arsenal, if he comes to us, great for us, if he goes to another club, great for them."
Some media reports on Monday speculated that Chelsea could make an attempt to persuade Sanchez to stay in London rather than move to United while others have suggested that United midfielder Henrikh Mkhitaryan may be part of negotiations to bring Sanchez to Old Trafford.
The Armenian was left out of the squad against Stoke but Mourinho said his future was unclear.
"I understand that with so much talk and so much speculation it is not easy for Mkhitaryan to play, to play at home with this feeling that it can happen, maybe doesn’t happen," said Mourinho.
"I prefer to protect him and protect the situation and at the end of the transfer market, if he stays here, he is a very good player, one that started this season very, very well and come a bit down. But last season did amazing things for us, helped us to win the Europa League being one of the most important players. Let's see what happens," he added.
Sanchez was left out of Arsenal's squad for their 2-1 defeat at Bournemouth on Sunday, with Wenger saying a decision on the Chilean's future was "imminent".
"Yes (it's imminent). Don't read too much in it because even I don't know which way it will go," said the Frenchman.
"He's being vague at the moment. The situation is not completely decided one way or the other, so I left him at home."
Sumber City drop Sanchez interest as Mourinho waits