De Gea has been Solskjaer’s first-choice throughout his tenure to date, though the 29-year-old’s place has come under scrutiny of late following a mixed campaign which has included several high profile errors.
Henderson, meanwhile, has greatly impressed while out on loan at Sheffield United and Romero has proved to be an able deputy during United’s domestic cup and Europa League campaigns.
Ahead of Monday’s Europa League quarter-final against Copenhagen, Solskjaer hailed all three goalkeepers and veteran back-up Lee Grant, at one point describing himself “the most privileged manager in the world”.
Yet the Norwegian also admitted that he will be unable to give adequate playing time to each of De Gea, Romero and Henderson when all three are available to him next season.
“I think as you say, competition for places is important and we’re looking to have competition for places,” Solskjaer said.
“We have Dean, Sergio and David at the moment in the ranks. Lee, the fantastic professional he is, is backing them up. But it’ll be difficult obviously to keep three of them at the club, so we’ll see what the decision will be there.”
Despite returning from his loan at Sheffield United, Henderson was ineligible to play in the Europa League mini-tournament to be held in Germany over the course of the next two weeks.
Another year on loan at Bramall Lane is one possibility for Henderson, who is understood to be in negotiations with United over a new contract, though the 23-year-old is eager to prove himself under Solskjaer.
The United manager also faces a decision over whether to stand by Romero – his ‘cup goalkeeper’ – for the latter rounds of the Europa League or to reinstate De Gea.
Asked whether Romero would start against Copenhagen, the United manager said: “That’s an obvious question. I must be the most privileged manager in the world with goalkeeping department.
“Sergio, David, Dean Henderson coming up, three top top goalkeepers and this Europa League has shown how important Sergio has been for us and David has always been performing. We’ll see what we’ll do and going forward.”