The midfielder was conspicuous by his absence from the squad for Saturday’s 1-0 win against West Brom, but should shake off a knock to face the Turkish side.
“We hope he’s going to be available,” Solskjaer said. “He trained this morning. See if there’s any reaction when we report tomorrow.
“Still Luke Shaw is out, Phil Jones is out. Jesse [Lingard] is still self-isolating after being in contact with a positive (coronavirus) case.
“There’s one or two little things we need to look at in the morning but hopefully everyone else is available.”
Dean Henderson made his European debut against Basaksehir in gameweek three and has since gone onto make his senior England bow.
But the 23-year-old is the clear back-up to David De Gea, potentially putting his progress and European Championship hopes in jeopardy.
“I’ve been very happy with the competition that Dean has provided for David and the response from David,” Solskjaer said.
“Dean’s not really put a foot wrong and he’s developing and he’s maturing along the way, which I’m very, very happy with.”
Solskjaer would not confirm Tuesday’s starter but says Henderson will continue to get opportunities this season at United.
Manchester United’s Ole Gunnar Solskjaer says Champions League defeat to Istanbul Basaksehir was ‘a punch in our stomach’
“Dean wants to stay at Man United and play for Man United,” he said.
“I can’t see the logic in (suggestions there is) only one potential appearance left before Christmas. Do you know how many games we’ve got?
“I disagree completely if (you are suggesting) tomorrow is a make-or-break (moment) for Dean.”
Predicted Manchester United XI (4-3-3): Henderson; Wan-Bissaka, Maguire, Tuanzebe, Telles; McTominay, Van de Beek, Fernandes; Rashford, Greenwood, Cavani
Additional reporting by Press Association.