Kompany has reportedly been selected as part of a four-man shortlist to replace Graham Potter as Chelsea manager.
The former Manchester City captain has guided Burnley to Premier League promotion in his first season in charge and has been hailed for his attractive style of football.
Chelsea have placed Frank Lampard in interim charge for the rest of the season.
"Are they interested in him because they've seen what he's done at Burnley, they've studied it and they think he's the right man for what they need?" asked Reo-Coker on BBC Radio 5 Live.
"Or is it again that Todd Boehly has seen something shiny and that everyone is talking about him and thought 'let's go for him'?
"That's the problem at Chelsea, I don't see good leadership and them going after managers for the right reason and right purpose.
"If I was Vincent Kompany I'd be flattered but wary of going because right now, for me, that club is toxic."
As a player, Kompany joined Man City from Hamburg in 2008 and starred for eleven seasons, making 323 appearances and captaining the side to four Premier League titles, two FA Cups and four League Cups.
