The two reportedly met for three hours to get to know one another.
Bylsma also spoke with former Winnipeg Jets coach Claude Noel about the 23-year-old forward.
As for what Noel told Bylsma?
“There is probably not a guy who is more competitive than Evander Kane,” Bylsma told Sportsnet’s Elliotte Friedman.
Bylsma has also considered the idea pairing Kane alongside Jack Eichel the projected No. 2 selection at next month’s NHL Draft.
“If that can work, imagine it coming at you,” Bylsma said of the pair’s speed.
Bylsma had an up close look at Eichel when the two were with Team USA at the World Hockey Championship in the Czech Republic.
“Right away in the tournament — versus Finland, versus Russia — he showed he could play against men, 16-18 minutes,” said Bylsma. “There were times he skated right by them…special plays from a special player.
“From what we know, (Eichel’s) power numbers are extremely good. His vertical, again from what we know, would be the second-best among the Sabres…so there’s a powerful base. He still needs to work on strength and to get bigger, but what he generates is an enormous amount of power. The way he can accelerate, you don’t see someone do that every day.”