Edinson Cavani could return for Manchester United in their Premier League fixture against Crystal Palace on Wednesday night.
Cavani, 34, has not played since the draw with West Brom on February 14 and missed the last four games with a muscular injury, but he trained with the squad on Tuesday morning and is in contention to travel to London.
However, Phil Jones could be sidelined for the rest of the season with a knee injury. Jones, 29, has not played for United since January 2020 and sustained his latest injury in June.
Paul Pogba (thigh) could struggle to figure for United again this month as there are internationals the week beginning March 22.
"We've had a training session this morning," Solskjaer said. "Of course, it was a light one and we're looking okay. There are a couple of doubts for tomorrow that we have to give as much time as possible. Edinson trained, he's joined in, that's good, let's hope there's no reaction after the session and hopefully he will travel with the squad.
"With Phil, obviously we hope [he will play again this season]. He's working really hard, he's had a couple of setbacks and it's just that kind of injury you have to be patient with and give him time. I know all about these injuries (Solskjaer had a recurring knee problem for three-and-a-half years).
"I'm not sure [when Jones will be back], how long is a piece of rope? That's how I felt as well, when I came back. We'll give him absolutely every chance this season, if not the start of next.
"Paul is still not ready for us, he's feeling better, he's not been training with the team yet, so he's definitely not travelling down to London."
