However, there is still work to be done for both sides to come to an agreement on a contract extension.
"Certainly, there's a tremendous amount of work that needs to be done and behind the scenes there's lots of work that is ongoing with Evander's basis and others on a parallel basis as well," Cheveldayoff told the Sun.
In 74 games with the Jets this past season, Kane recorded 30 goals and 27 assists for 57 points.
Meanwhile, Cheveldayoff is also expected to pursue talks to get their backup netminder on board for next season.
It remains to be seen with which goalie they will agree, either Chris Mason or Jonas Gustavsson, or if both will become unrestricted free agents on Sunday.