It's believed contract negotiations have started between the Red Wings and Datsyuk's agent, albeit only preliminarily.
The two sides have at least one month to finalize a deal, as an extension cannot be formally signed and announced until July 5.
Datsyuk, who spent the lockout in the KHL, would eventually like to finish his playing career in Russia, but only after he's done at the NHL level.
Datsyuk's seven-year, $46.9 million contract expires after next season. It's unclear what type of contract he's looking for, but could see his salary in and around the same $6.7 million he'll make next season.
In 47 games with the Wings this season, Datsyuk led the team in scoring, registering 15 goals and 34 assists for 49 points.
The four-time All-Star has played in 779 career regular-season NHL games, all with Detroit, and has accumulated 255 goals and 512 assists for 767 points.
Meanwhile, the Red Wings must also focus on signing impending unrestricted free agents Valtteri Filppula and Damien Brunner.
Filppula and Brunner are due for raises and could command significant interest on the open if they go unsigned by July 5.