The former Blues chief believes the Portuguese would give any team the "maximum chance of winning" but indicated his differences with Roman Abramovich could make a return difficult
The 50-year-old won six trophies in three years with the Blues, including two successive Premier League titles, and is rumoured to be on his way back to west London after a troubled spell with the Spanish giants.
Kenyon expects the club to look at a number of candidates, including Malaga's Manuel Pellegrini, but indicated the self-proclaimed 'Special One' would definitely be his number one choice.
"If I was at another club and looking for someone who would give me the maximum chance of winning, it's Jose Mourinho," he told BBC Radio 5 Live.
|18/1||Chelsea are 18/1 with Bet365 to beat Manchester United 2-0
"I'd need some other very strong candidates to look elsewhere and you'd have to say he's very much on the shortlist.
"Pep Guardiola would have been up there [as a candidate] but he's not available. Manuel Pellegrini you would definitely look at. But if I was looking at Pellegrini or Jose, Jose would win hands down."
Mourinho left Stamford Bridge in 2007 by mutual consent but his disagreements with club owner Roman Abramovich were well documented and Kenyon acknowledged the need for the duo to clear the air.
"They're both very strong individuals and before this appointment happens, if it happens, there will be an awful lot of discussion between those two," he continued.
"It's a very different team now, that is at a very different part of its evolution as a major European team, and clarification is needed over players.
"Given the past history that they both know each other, they have both worked with each other, all that does is heighten the need for some of those things to be ironed out before the appointment is made."