United boss Mourinho said on Wednesday that the Italy international could leave Old Trafford 'but not at any price'.
The 28-year-old, who has struggled to cement a starting place since joining from Torino in 2015, then confirmed his intention to seek a new club.
Speaking to a number of national newspapers, Darmian said: 'I want to play more regularly. Last season, I didn't play much, that's my objective and my ambition.
'That's why I spoke with the manager and also with the club about my future. I want to leave but we will see what happens because we don't know.'
Darmian, who started just five Premier League games last season, has been linked with a return to Italy.
When asked if Serie A would be his preferred destination, he said: 'It's an option. Yes, probably.
'We will see what happens. Honestly, I'm waiting. If I stay, I stay and I do what I did up until now. If I go it is because the offer that another team makes will be good.'
Darmian's potential departure could leave Mourinho short of a right-back ahead of the new season, with Antonio Valencia and new signing Diogo Dalot both injured.