Although the 33-year-old goalie could end up staying in Vancouver, the Leafs could potentially become a contender to acquire the netminder if a reasonable deal can be done.
Meanwhile, two others goalies are likely to be on Burke's radar in his quest to upgrade the goaltending in veteran pending unrestricted free agent Tomas Vokoun of the Washington Capitals and young Nashville Predators backup Anders Lindback, who is slated for restricted free agency on July 1.
However, the Philadelphia Flyers are also reported to have interest in Vokoun, who could bring a better veteran presence than Sergei Bobrovsky to Ilya Bryzgalov.
It was also reported that Vokoun turned down a lucrative offer from the KHL to stick around the NHL and see where he could be a good fit.