The Red Devils need to pick someone to succeed Antonio Valencia who is leaving Old Trafford this summer.
And Young is expected to be the man who is given the armband by Solskjaer.
Some reports claim the Norwegian could offer Paul Pogba the role though in a bid to keep him at Manchester United beyond the current campaign.
But the news of Young on the verge of being appointed captain has left fans furious with Solskjaer.
One said: “Ashley Young as captain? Who can stand the sight of that guy’s name in the first team sheet? If all ManUtd does this summer is release him for free, then we’ll have had a successful xfer window.”
Another added: “So Ashley Young’s would be Manchester United Captain 2019-?? Disgraceful.”
A third explained: “I do hope the latest rumour that Ashley Young is going to be made full time captain is a joke if it’s not then I’m 100% ole out.”
Young was much criticised for his performances as United struggled at the end of the season.
The Red Devils ended up finishing sixth in the Premier League and will therefore compete in the Europa League next year.
Solskjaer is set to overhaul his side as a result but it appears Young will be going nowhere.
The 33-year-old was first choice at right-back for United this season, ahead of Diogo Dalot, Matteo Darmian and Valencia.
United have been linked with a number of transfer targets.
Aaron Wan-Bissaka, Sean Longstaff, Declan Rice and Daniel James are all on Solskjaer’s radar.
Swansea star James is close to joining United with a £15million agreement repeatedly agreed between the clubs.
The 21-year-old made 38 appearances in this season, netting five goals and providing 10 assists.