"Hopefully if things go right, I'll get my opportunity," Bowe said following his 45-minute meeting with Tyson at the Indiana Youth Center. "But I want Mike at this point to relax and just take it easy and hopefully we can get together.
"Mike is the best heavyweight out there, as far as I'm concerned. It will be a dream for myself to face Mike. Not to mention there will be a whole lot of money involved."
Bowe knocked out Herbie Hide in the sixth round on Saturday night in a World Boxing Organisation heavyweight title bout in Las Vegas, but he had to knock down the much smaller Briton seven times to accomplish it.
Once Tyson, 28, leaves the Indiana Youth Center, he plans to return to Cleveland. After that, he will remain on probation for four years. There are no legal restrictions that might prevent him from resuming his boxing career.
"Mike looks in excellent shape," Bowe said. "He's in a good state of mind and I think he'll be a force to be reckoned with."
Bowe said no definite plans were made, though the two talked about fighting at Madison Square Garden in New York.Reuse content