Old Trafford midfielder Fletcher has not featured for the Red Devils for almost a year as he continues to battle a serious ulcerative colitis condition.
But he completed a 90-minute run out for the club's reserve side against Stoke earlier this month and could be ready to resume his playing career.
Solskjaer was a team-mate of Fletcher in his final years as a Manchester United player and was part of the Norway side which provided the opposition when the 29-year-old made his bow for Scotland.
The retired frontman - now managing Molde in his homeland - recently met Fletcher in Manchester and was left feeling optimistic about the 29-year-old's future.
He said: "It's fantastic news that Darren is on his way back. I was over in Manchester about a month ago and I was lucky enough to bump into Fletch and he said he was on the road to recovery.
"I just met him purely by chance outside the supermarket and it was great to see him. I could see just from talking to him that his tail was really up because he's had a rough time of it obviously.
"It's funny to think I played in his Scotland debut in Oslo. I remember that game well, we actually swapped shirts afterwards and I've still got it at home - I was thinking of digging it out and putting it on for the game on Tuesday night.
"I actually played in Fletch's reserve team debut for Manchester United, I was in the reserves quite a lot.
"I'm not sure he was even 16 at that time but I remember it was a game at Everton and you could just see then that you were watching a fantastic talent.
"He'd had loads of injury problems but I knew the manager had really, really good faith in him and I could see even in that very first reserve game just why Alex Ferguson had such high hopes for this kid.
"I've followed his career from that day on because I knew he was a special player but also because he is a good guy.
"I admired his mentality, he was never in awe of the place and he just felt at ease and felt at home at Old Trafford.
"He had confidence in himself but he was humble. He had a tremendous work rate as well and the thing that stood out for me was the way he almost floated on the pitch, gliding through games.
"It came naturally to him and made the hard part of the game look easy. I knew Fletch was going to be a legend for Scotland and hopefully now he'll get back fit and improve even further to become a better player.
"To be honest I do know how hard it must be for him because I had a spell out for two and a half to three years myself after a bad knee injury.
"There's nothing worse than that feeling of not really knowing whether you're going to be able to make a comeback but luckily now it looks like it's going to happen and I couldn't be happier for him.
"He's a humble guy from a humble family - he possesses all the attributes to be a Manchester United player. I've heard the accusation that he was an average player in a great team but I don't agree with that at all.
"We used to play Darren against the likes of Arsenal - in the big games, semi-finals - and he just ran more than them.
"You could see Patrick Vieira never liked playing against Fletch and that to me is the sign of a great player.
"For me, the proudest moment in my career was when I made my comeback from injury, scored for Manchester United and my son celebrated by clenching his fists.
"Fletch has got his own twins so I'm sure he'll want to play to show them he's a good player. When I met him recently he seemed very positive so I'm sure it's going to happen."