Old Trafford chiefs believe Ibrahimovic will sign the fresh deal this week, according to ESPN.
The 35-year-old - out of contract since July 1 - is recovering from a knee ligament injury ahead of schedule.
It was initially thought he would be out until early 2018.
Ibrahimovic has been undergoing rehab at the club's training complex.
Jose Mourinho wanted the Swedish legend to remain at the club.
Ibrahimovic bagged 28 goals last term but also impressed Mourinho with his influence in the dressing room.
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ESPN report that the new deal will earn him less than his previous contract.
Ibrahimovic has snubbed a move to LA Galaxy to rejoin United.
When he returns to full fitness, Ibrahimovic is likely to play a back-up role.
Romelu Lukaku is Mourinho’s main man following his big-money move from Everton.
While Marcus Rashford and Anthony Martial have impressed in the opening weeks of the season in support of Lukaku.
Ibrahimovic’s return provides Mourinho with extra depth for what is likely to be a busy campaign.
Meanwhile, Steven Gerrard has suggested United have a squad capable of challenging for the Premier League title.
But the Liverpool legend warned: “I still think they need a top-class left-back.”
