Kenyon, who was part of United’s board for six years, became chief executive at Chelsea in 2003 and a year later was responsible for brining Jose Mourinho to Stamford Bridge.
However, the 65-year-old thinks United have made an error when they sacked the ‘Special One’ and replaced him with Solskjaer.
Kenyon also thinks United didn’t do enough off the field to help Mourinho succeed during his time at Old Trafford.
No one better than [Jose Mourinho] knows what United represents
Peter Kenyon
“The key is give him the adequate structure and organisation to make sure he’s a part of everything,” Kenyon said at the World Football Summit.
“I was the first to express my disappointment when he left United because I think he could have been a part of that great leadership structure.
“No one better than him knows what United represents. José is far from being an irrelevant and outdated manager.”
United made a strong start under Solskjaer, while he was their interim manager, and after winning 14 of his 19 matches in charge, he was given the role on a permanent basis at the end of March.
Man Utd news: Peter Kenyon is the former CEO of United and Chelsea (Image: GETTY)
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However, United’s form dropped at the end of last season and the Red Devils ended up missing out on qualification for the Champions League as they finished sixth in the table.
Solskjaer is now under pressure this season after only picking up eight points from six Premier League games and the struggles at the club haven’t been helped when United needed penalties to beat League One side Rochdale in the third-round of the Carabao Cup.
And while Solskjaer ponders on how to close the 10-point gap on league leaders Liverpool, Mourinho is working as a TV pundit as he awaits his next managerial job.
And Kenyon insisted Mourinho would be the first name on his list if a big club needed a new manager.