Manchester United duo Paul Pogba and Marcus Rashford will be available for selection if the green light is given for the Premier League season to resume next month.
The pair had been long-term absentees prior to the campaign being brought to a halt by the coronavirus pandemic in March, but both players returned to small group training last week.
Competitive action could restart in England's top flight in mid-to-late June and United boss Solskjaer revealed Pogba and Rashford came through their first few non-contact training sessions unscathed.
"They're looking good. They've joined training now and they've done everything the other boys have been doing. There's been no reaction so far, touch wood," Solskjaer told MUTV.
"When we get started, it looks like we can have a full squad to choose from."
United's players had spent the previous two months training alone, but Solskjaer has no complaints about their fitness and is hopeful he can take the next step to full-contact training.
"The players have been looking after themselves," he said. "They've done well. Charlie [Owen] the fitness coach, Kieran [McKenna], Michael [Carrick] and Martyn [Pert] have been on to them all the time. They've not had many days off!
"There have been video calls and of course the last couple of weeks they’ve been stepping it up.
"The boys have been fantastic, the weather's been good and they've enjoyed it.
"Hopefully now we've proved we can do this safely and we can move to the next step. It's been really enjoyable being on the training ground again.
"Everyone's looking sharp, everyone's been in with a good mood and we've been splitting up in groups so [working in] fours and fives together and they've really done well.
"Hopefully, they can as I said, step up and go to bigger training groups but so far it's been good."