Manchester United scouts are impressed by Maguire who has proven his World Cup form was no fluke after a fine season wth Leicester.
Solskjaer is keen to add Premier League experience to his side, something Maguire has.
The reports also claim Napoli have rejected all advances for Koulibaly so far.
United are looking to overhaul their side this summer with several defenders uncertain of their future at Old Trafford.
Man Utd are ready to target Harry Maguire again this summer (Image: GETTY)
Gareth Bale would've fit perfectly at Man Utd claims pundit
Man Utd boss Ole Gunnar Solskjaer will overhaul his side this summer (Image: GETTY)
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Phil Jones, Chris Smalling, Eric Bailly and Marcos Rojo could all be deemed surplus to requirements.
Victor Lindelof has been the only consistent performer for United in defence this season.
Solskjaer was fuming after the 1-1 draw with Huddersfield at the weekend and admitted that was it for some stars.
“I can’t talk about individuals now but there’s a chance you’ve seen the last of [some] players,” he said. “We weren’t good enough . . . the table seldom lies.
“Effort and attitude was not the problem. The players were running and trying. We just weren’t good enough. That is the problem.
Man Utd supremo Ed Woodward is ready to sanction big moves this summer (Image: GETTY)