It sounds as though Evander Kane's only priority now is to be able to compete for a Stanley Cup. There also seems to be a thought being shared that Kane isn't interested in anything other than a short term show me deal. That means Kane's top priority is likely entering a situation where he can play with a star player in hopes of inflating his value on his next deal.
According to TSN's Gord Miller the timeline for Kane's signing is expected to be a short turn around. Miller believes according to those he's spoken with that a deal will be done by the end of the week.
This timeframe would allow a team that signs Kane to get the winger into the lineup by the beginning of February once he's caught up with the team.