De Gea has been Solskjaer's regular first-choice for much of the campaign but has lost his place to Henderson after returning to Spain to attend the birth of his child.
Henderson was picked for the 2-1 win over Brighton on Sunday with De Gea forced to watch from the bench but Solskjaer insists the battle for the gloves is not over.
"When you are a part of Man United there are always going to be players coming in that don't just come to fill the bench," Solskjaer told a news conference on Wednesday.
"Everyone has ambition to take your shirt. I was there myself as a striker. We signed Ruud [van Nistelrooy], Diego Forlan, Louis Saha, loads of top strikers, Dwight Yorke and Teddy Sheringham. The aim for me then is to prove to the manager that 'ok I don't mind you signing these but I'm still important for you and I'm still going to give everything I can to play'.
"David has had 10 fantastic years at Man United and he's had challengers. Of course they want to play. Sergio [Romero] probably played less games than he deserved, Dean has come in and given it his all because everyone wants that place in the team. David does as well and it's a healthy competition.
"If it's Dean or David, I'm very comfortable with both of them to play and I'm very happy that none of them are happy to not play."
"Marcus is travelling," Solskjaer said, who has included 18-year-old striker Anthony Elanga in his squad for the trip to Spain. "We've got to make a decision tomorrow [Thursday] if he starts or if he's on the bench. I don't think he'll be a 90-minute man.
"Anthony has started his recovery. If we see him before the end of the season I'll be very surprised but he's determined to come back as quickly as he can."