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The 23-year-old is currently spending a second season on loan at Sheffield United and has impressed during his debut campaign in the Premier League.
He has yet to make a senior appearance for his parent club and had loan spells at Stockport County, Grimsby Town and Shrewsbury Town prior to linking up with the Blades.
His performances for Chris Wilder’s side this term have been a key factor in the Blades sitting in seventh place in the table and pushing for Champions League qualification in their first year back in the top-flight.
Victory over Aston Villa on Wednesday on the Premier League’s return from the coronavirus-enforced hiatus would also see them leapfrog United in the table, with reports suggesting Henderson will be allowed to complete the campaign at Bramall Lane.
Where he will be playing next season is still to be determined, but Solskjaer has no doubts that Henderson will eventually be first choice at Old Trafford.
"Dean has made some great choices over the years and has developed fantastically," said Solskjaer. "We're looking at that in terms of where he's going to be next season, but as yet that has not been decided.
"This season has proved a great experience for him, he's done himself some favours with his performances, and proved he will be England's No.1 and Man United's No.1 at some point."
Currently blocking Henderson’s path at Old Trafford is David de Gea, who has been United’s first-choice keeper since joining from Atletico Madrid in 2011.
The Spaniard signed a new four-year contract at United last September, but Solskjaer is not concerned by the prospect of De Gea or Henderson feeling unhappy with their lot if the two keepers are jostling for the No.1 jersey.
He added: "It's not my job to keep the players happy or in the team or out of it. Part of it is their responsibility of performing and doing well.”
United will resume their Premier League campaign, and bid for Champions League qualification, with a trip to Tottenham on Friday.