He also owns a limited no-trade clause, where he can list up to 10 teams he will not accept a trade to.
It's unclear if the Maple Leafs have asked him to update his list, but according to one source, the Leafs have had a conversation with the Detroit Red Wings about Grabovski.
Several teams are looking for help up the middle, including the Anaheim Ducks, St. Louis Blues, Tampa Bay Lightning, Calgary Flames, Dallas Stars and Florida Panthers, though it's not known if these clubs have had conversations with Toronto regarding Grabovski.
The Leafs acquired center Dave Bolland from the Chicago Blackhawks on Sunday, further deepening their center position.
Leafs GM Dave Nonis and his staff have been in negotiations with center Tyler Bozak, who can sign with any team starting noon ET on July 5.
Bozak is believed to be seeking a long-term deal worth more than $5 million per season, something the Leafs are not willing to pay.
Toronto is, however, expected to pursue free agent center Stephen Weiss, who has spent his entire NHL career with the Florida Panthers, and will begin speaking to his camp as soon as teams are allowed to do so, at 12:01am ET Wednesday.
Meanwhile, the Maple Leafs are also entertaining calls for defensemen Carl Gunnarsson, Cody Franson and John-Michael Liles.