The former Sweden international made waves after arriving at Old Trafford in a free transfer switch from Paris St-Germain last summer.
However, he missed out on the chance to star in United"s Europa League final win over Ajax because of a serious knee injury suffered in April.
* TRANSFER NEWS LIVE: GOSSIP, DONE DEALS AND RUMOURS AS THE BREAK THROUGHOUT THE DAY *
That setback has left Ibrahimovic in need of a lengthy stint of rehabilitation following surgery in the USA in May.
And it meant United chiefs weren"t prepared to offer him an extension to the initial one-year deal he signed last July.
Jose Mourinho has opened the door for Ibrahimovic to make a Red Devils return once he gets back to full fitness though.
And The Sun claim the 35-year-old"s provided the clearest indication yet that he wants to play for United again.
They say Ibrahimovic"s sons Maximillian and Vincent will stick with United"s youth setup next season, despite his exit.
An insider told The Sun: "Ibra looks set to stay at the club and has even put his two children back into the youth system.
"It's the clearest indication yet he will remain here, but things might can always change in the future.
"The two young lads play in a youth group alongside [Ryan] Giggs and [Nicky] Butt's kids, they all get on very well."
Ibrahimovic will soon jet back to the USA to check-in with surgeon Freddie Fu in a bid to get the all-clear to step up his work at United"s training ground.
And The Sun reckon he"ll be handed a six-month contract towards the end of the year if he can prove he"s up to the job.
Mourinho is thought to be keen on having Ibrahimovic around, alongside summer signing Romelu Lukaku.
The Sun suggest his positive influence on young guns Marcus Rashford and Jesse Lingard is valued by the United gaffer as well.
