Ibrahimovic was released by United after suffering a cruciate knee ligament injury which brought a premature end to his debut season at Old Trafford.
The Swedish striker has been doing his rehab at United’s AON Training Complex and Mourinho admitted they could re-sign the 35-year in December, when he is expected to be fit again.
“It’s possible, it’s open,” said Mourinho. “Of course.
“We want him to be honest and open and let everything be there for him to make a decision in case his desire was to leave, so there was not a new contract.
“There was a space and time for everyone to think, to feel, to decide and, from his point of view, he made the decision to still want to play football at the highest level.
“It would be easy for him to hide behind such an amazing injury and say it’s time to play at a different level. But he made the challenge for him to continue at the highest level.
“We opened our door for him to recover with us and then to make a decision.
“If that decision is for him to stay and for us to wait, let’s say, until December, because I don’t think before December he can be back playing competitive football, then why not?
“We are speaking, we are exchanging ideas, but the most important thing is what is best for the player.”
On Romelu Lukaku, Ibrahimovic’s replacement, Mourinho was asked what the Belgium international will bring to United.
“What will he bring?” said Mourinho. “Hopefully goals.
“Everybody knows he is a striker, so we are not speaking about a multi-functional player or a player who can adapt, he’s a striker.”