Despite mutual interest between the Oilers and Brown, the forward is planning to explore the market to gauge his value.
The 30-year-old is set to become an unrestricted free agent on July 1 after playing on a one-year, $1 million deal this past season.
The Toronto native had 13 goals and 30 points in 82 games this past season and had another five goals and nine points during the Oilers run to the Stanley Cup Final.
Brown originally signed a one-year, bonus-laden deal with the Edmonton Oilers for the 2023-24 season, aiming to prove himself after recovering from a torn ACL that limited him to just four games the previous year.
The Toronto Maple Leafs drafted him in the sixth round of the 2012 NHL Draft. In 601 career games during the regular season, Brown had 107 goals and 258 points with Toronto, Edmonton, the Ottawa Senators and the Washington Capitals.