The England and Tottenham star is being linked with a move away from the North London club, given their lack of trophies and ability to challenge for the Premier League title.
The Athletic recently reported that Kane wants out, but Spurs chairman Daniel Levy will resist selling him to an English team.
Asked about Kane, Bridge told bettingexpert.com: "I'd love to see Kane go [to Chelsea], I think he's brilliant. Sometimes money talks.
"If you look at how Tottenham are doing at the moment, I think there's a great chance he could end up leaving if he wants to go and win something.
"I'm not sure if he would go, but I'd love to see him come in and start banging in goals for Chelsea.
"Chelsea have to be careful with who they buy but I'll be very surprised if they didn't bring another striker in."