Several teams have expressed an interest in Spezza, including the Anaheim Ducks, Nashville Predators and St. Louis Blues.
According to the Ottawa Citizen, the Florida Panthers and Phoenix Coyotes could also be in the mix for Spezza.
It's unknown which 10 teams the Mississauga, Ontario, native will not accept a move to.
Spezza, 30, has one-year left on his contract that pays him $4 million, though his salary cap hit is $7 million.
It's unclear what the Senators are asking for in exchange for Spezza, though a young center is believed to be part of their demands, which could also include a top-young forward prospect and a high draft pick.
In 75 games with the Senators this season, Spezza registered 23 goals and 43 assists for 66 points.
TFP first reported on March 3 that the Senators were exploring the market on Spezza.