But Henderson’s future could be linked to that of Sergio Romero, with the back-up 'keeper believed to have been particularly frustrated by his omission from the FA Cup semi-final last month.
Romero has largely been used at United’s cup keeper, even playing ahead of David de Gea when the club last won the Europa League under Jose Mourinho in 2017.
But he was dropped for the 3-1 Wembley defeat against Chelsea, having played in the quarter-final at Norwich.
Solskjaer has also made it clear the Argentine has little hope of displacing De Gea, insisting recently he’d never even considered taking his no1 out of the firing line even after a series of high-profile errors.
Romero is said to be frustrated about his situation and the amount of action he sees in Cologne for the truncated end to the Europa League could determine if remains happy to warm the bench.
Solskjaer is determined to stick with De Gea as his long-term first choice, despite Henderson’s outstanding form on loan at Sheffield United.
The preference is to allow him to develop further with another loan spell, with the Blades already opening discussions with United over a new deal.
Solskjaer is open to that, but could be forced into a rethink depending on Romero, who he refused to assure of a place in Monday’s quarter-final against FC Copenhagen.
He said: “I think I must be the most privileged manager in the world with the goalkeeping department, with Sergio, David and we’ve got Dean Henderson coming back. Three top, top 'keepers.
“This season has shown how important Sergio has been for us and for me David always, always performing. We will see what we do for the rest of the season and going forward.
“It’s difficult, but it’s a nice problem to have.”
Solskjaer added: “Competition for places is important. We are looking to have competition for places.
“We have Dean, Sergio, David in the ranks. Lee (Grant), the fantastic pro that he is, is backing them up.
“It will be difficult to keep three of them at the club, so we will see what the decision will be there.”
Romero has started 16 games this season, but none in the Premier League.
He played in the second leg of United’s Europa League last-16 tie against LASK on Wednesday, but Solskjaer admitted afterwards that he would turn to his star players in the later rounds.