The 35-year-old joined United last summer on a one-year contract and enjoyed a profitable first season in English football, scoring 28 times in 46 appearances in all competitions.
A cruciate knee injury towards the end of the season has kept him on the sidelines ever since, however, and as a result United opted not to take up a one-year extension on his £375,000-a-week deal.
The Swede has been working on his rehabilitation at United and, speaking to the media today, Mourinho confirmed reports of negotiations for a new deal.
"He is injured, he needs time to recover, he's not ready to play tomorrow," he said. "It's not something urgent, that we are desperate to get it done or not done.
"I just think that he was very clear by showing what he did last year, it was not enough for him. He thinks he can do more and he wants more at football's highest level.
"So we are having conversations and we are discussing the possibility of staying with us for the second part of the season."