Ole Gunnar Solskjaer does not expect any Manchester United players to leave before Thursday's transfer deadline, but would not rule out late departures.
There has also been speculation Brazilian midfielder Andreas Pereira, who has been loaned to Spanish clubs Granada and Valencia in recent seasons, could make another temporary move.
"At the moment I can see everyone staying at the club," caretaker coach Solskjaer said at his press conference ahead of Tuesday's Premier League visit of Burnley when asked about reported Juventus target Darmian's situation.
"No deals have been done with anyone but there are still a few more days.
"I’m not too involved in the negotiations so whatever happens happens, but it’ll be good to get the window closed and keep improving the players in the squad still here."
Pereira, 23, something of a fans' favourite with the United support, enjoyed a handful of early-season performances under previous manager Jose Mourinho, who was sacked in December.
His opportunities dwindled, however, and he has had few chances to impress Solskjaer yet.
But the Norwegian ruled out another loan and says his chance will come.
"I can’t see him going out on loan because Andreas has done fantastic in training ever since I come back," he said.
"He’s a player I can see playing quite a few games for us towards the end of the season."