Several teams, including the Anaheim Ducks, Calgary Flames, Washington Capitals, Tampa Bay Lightning and Detroit Red Wings, had expressed an interest in Grabovski, though its unclear which teams are still in the mix.
According to Craig Custance of ESPN, Grabovski's agent Gary Greenstin told him three teams are "very interested" in his client.
Custance also indicated, though, that a decision is not expected to be made until August.
A number of teams are looking to make trades in order to free up some salary cap space or create a roster spot, and that has affected some free agents, like Grabovski, from signing.
In 48 games with the Leafs this past season, Grabovski registered nine goals and seven assists for 16 points.
In 367 career NHL regular-season games with the Montreal Canadiens and Maple Leafs, Grabovski registered 94 goals and 123 assists for 217 points.
Drafted by the Habs in the fifth-round (150th overall) in 2004, Grabovski was traded to Toronto on July 3, 2008 in exchange for Greg Pateryn and a second-round pick.