The Chile international is widely expected to leave the Gunners either this month or at the end of the season, when he can depart for free due to his contract expiring.
Manchester City were initial favourites to add the attacker to their squad, but reports have claimed that the North-West outfit have withdrawn their interest due to an unwillingness to pay more than £20m to Arsenal.
United were thought to be in the driving seat over the last few days, with reports emerging that they have handed the number seven shirt to Sanchez, but now it has been claimed that Chelsea have entered the race.
After securing a comfortable 3-0 victory over Stoke City this evening, Mourinho was asked about the status of the Sanchez situation.
"No news on Alexis Sanchez, 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," the United boss told BBC Sport.
While speaking to Sky Sports News, Mourinho said: "I've no idea. Today I was completely separate from all of that - I was just focused on my match and not worried about anything else.
"I'm not going to speak about hypothetical situations. Probably there are other clubs also interested and trying and I shouldn't talk about a player who is an Arsenal player."