Sanchez nearly joined City for about £60m on the final day of the summer window, only for the transfer to collapse when Arsenal failed to sign Monaco and France midfielder Thomas Lemar.
Mourinho added that "we believe that there are some players that if you have a chance to sign them, no matter the month, then you have to try", per football writer Chris Winterburn.
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The finale witnessed top two finalists- Hina Khan and Shilpa Shinde in the faceoff to lift the trophy. As a result, he has been evicted from the show becoming the second runner-up of the reality show.
The 20-year-old's potential has attracted interest from the Premier League with Arsenal and Tottenham strongly linked with a move for the South American attacker in recent weeks. As a manager, you have a lot of things to deal with, and you have to choose which one you want to be focused on. The players have two choices: Follow what you [the media] say, or follow me.
"At this stage, I don't think it's about the market", said Mourinho, whose United hosts Stoke City on Monday.
United are said to have made a £25m (€282.m) bid for Sanchez on Thursday (11 January), with reports claiming Mourinho is confident his side can beat neighbours Manchester City to one of the biggest deals of the January transfer window.
"Of course I want a quick resolution", he told reporters at Arsenal's north London training base. If Pep wants him again now, I'm sure he's thinking: 'I'm going to go there second time round and do it properly this time. However, with three competitions still in play it is hard to see how Arsenal can avoid it, if indeed Walcott and Sanchez both leave. Certainly not, but there's always a way to find a different balance. Guardiola, though, wants nothing to distract his players as they prepare for Sunday's Premier League visit to Liverpool, and continue their pursuit of four trophies.
City are willing to pay Sanchez £285,000-a-week while United are happy to go over £300,000-a-week in order to usurp their Manchester rivals.
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