Vanek, 30, is in the final-year of a seven-year, $50 million contract he signed while playing with the Buffalo Sabres, a team that traded him to the Islanders earlier this season.
Islanders GM Garth Snow is looking for a young, NHL-proven forward with top-six potential as the centerpiece of a package, which will likely include a high draft pick and a top prospect, for Vanek.
Snow has been in ongoing trade discussions with Los Angeles Kings GM Dean Lombardi over Vanek, though talks have also included left wing Michael Grabner and defenseman Andrew MacDonald, who, like Vanek, is also set to become an unrestricted free agent July 1.
The Kings are battling the salary cap, which might prevent a trade from happening prior to Friday's Olympic freeze. The Pittsburgh Penguins and Detroit Red Wings are among the teams also eyeing Vanek, but have the same financial restraints as the Kings.
According to multiple league sources, the Islanders are interested in young left wing Tyler Toffoli and defensemen Alec Martinez and Jake Muzzin of the Kings.
If the Islanders want to trade Vanek before Friday, which is their preference, they might be forced to pay some of his remaining salary.
Grabner, who might be a more flexible option under the cap, has two-years left on his contract, beyond this season, at a salary cap hit of $3 million.