The Toronto Maple Leafs granted Hyman permission to meet with other teams earlier this offseason to explore trading his rights. A sign-and-trade is possible until free agency opens July 28, so the Oilers could potentially add the winger on a maximum eight-year deal, notes Sportsnet's Chris Johnston.
The Calgary Flames and Vancouver Canucks are among the other teams reportedly pursuing Hyman, who produced at a 63-point pace this past season as a staple in Toronto's top six.
Hyman is coming off a four-year contract that paid him $2.25 million per season; the 29-year-old is expected to land a significant raise.
Edmonton has $11 million in projected cap space, according to CapFriendly. The club is reportedly on the verge of re-signing goaltender Mike Smith to a two-year with an average annual value of around $2 million. The Oilers also lost defenseman Adam Larsson to the Seattle Kraken on Wednesday.