Steven Stamkos hasn't yet begun to negotiate with the Tampa Bay Lightning on a potentially long-term extension yet, per several sources citing his agent, Don Meehan.
This isn't really news; we knew since the beginning of the playoff run (really, earlier than that) that the Lightning and Stamkos hadn't had any discussions at all about a new deal during the season. Both sides were focusing on the task at hand -- winning a Stanley Cup, something they came very close to doing.
Following the defeat at the hands of the Chicago Blackhawks in 6 games in the Final, Stamkos' next move wasn't "go talk to my agent and start working on a new deal".