Fletcher is battling to recover from a serious ulcerative colitis condition.
The Scotland international is reportedly close to making his return to action.
Solskjaer 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.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
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