He suffered ligament damage in his knee in a Europa League match against Anderlecht in April this year and was ruled out for the remainder of the season and at least the first half of the new campaign.
Ibrahimovic's one-year deal at Old Trafford expired in June and was not extended following the injury.
However, after playing a role for Real, Mourinho publically stated it was game over as it was clear the Spanish club wanted to keep hold of him.
"He thinks he can do more and wants more at the highest level, so we're having conversations and we're discussing the possibility of him to stay with us for the second part of the season".
After Ibrahimovic's season ending injury, the Manchester United boss had to rely on youngster Rashford to produce the goods.
This much was self evident, when United's new No.9 - the number which Ibrahimovic occupied last season - Romelu Lukaku deemed it necessary to seek the Swede's permission before taking his desired squad number.
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"I will just go with everything I have to try to win every match we play".
The Portuguese boss also disclosed that he will be without three players for Sunday's Premier League opener against West Ham.
"But we have lost important players to injury too, such as Marcos Rojo, Ashley Young, Luke Shaw, and Zlatan Ibrahimovic". He thinks he can do more.
Bale himself insisted he was happy in Spain and was unmoved by any speculation, focused on proving himself and getting the season started.
"So I don't think I am in a position of crying, of moaning, of protesting".
Romelu Lukaku, Victor Lindelof and Nemanja Matic have so far arrived this summer, but Mourinho always meant to make four acquisitions.