A few teams, including the Montreal Canadiens and Philadelphia Flyers, spoke with the Jets during last summer's NHL Draft, but were unable to come to terms on a trade.
Kane has four-years left on a six-year, $31.5 million contract and will earn $6 million in each of the next four seasons.
It's believed Cheveldayoff is willing to part with Kane, who does not own a no-trade clause, but the return must be significant in order for the Jets to make a move.
The Jets are not interested in selling Kane away for draft picks and prospects. According to a league source, Cheveldayoff will want an offensive top-six forward and a young, proven NHL-caliber forward included in a package for Kane.
While a trade is not guaranteed, trade talks are expected to pick up closer to the NHL Draft in late-June.
Meanwhile, Cheveldayoff will explore the possibility of re-signing center Olli Jokinen to an extension.
Jokinen is scheduled to become an unrestricted free agent July 1.