The former Whites midfielder has been linked with the top job at Elland Road following their relegation from the Premier League.
With Javi Gracia being sacked in April, Sam Allardyce was the man selected to lead Leeds into their final four matches of the season as caretaker boss, a position that Bowyer admitted exchanging messages about.
Appearing on the White and Jordan show, he said: "Without going into too much detail, there was a message or two exchanged, but the decision from the club was to go with Big Sam because of experience.
"Unfortunately for the football club that didn't work out, but going forward, I'd like to think that we would have a conversation at some stage and maybe try and put something together."
Now back in the Championship, Leeds face the pressure of securing an immediate return to the Premier League despite coming up against a second tier that is brimming with big names from English football.
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Bowyer has Championship experience with both Charlton and Birmingham and openly admitted that the job at Elland Road would appeal to him.
Pressed by Jim White whether he'd jump at the chance to manage Leeds, Bowyer remarked: "Oh for sure, I have a connection with the club and I understand the club and I think that's important for whoever goes in there next.
"But if I got the call, I would love to go there and get that club going again and get the fans onside and get the place bouncing again.
"I would definitely jump at the chance for sure."
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He added: "I know the Championship now, I've done a few years of management there, I understand it, I watched it all last season, and you analyse and see what it takes to get promotion.
"I believe if I went in there I would get them promoted again."