Nash, a two-time NBA MVP, has spent the past eight seasons with the Phoenix Suns, but has made it a point in recent interviews to stress that he's "open to everything" and says he'll listen to any team that calls.
However, industry sources monitoring the free-agent market have identified Toronto as one of four teams that pose the greatest danger to the Suns in terms of signing Nash away, including the Dallas Mavericks, New York Knicks and Brooklyn Nets.
Sources close to the process said Nash met with Knicks representatives on Sunday and that the Nets have requested a meeting with Nash and will speak to him Monday morning.
The Nets have interest in Nash both as a prime replacement for Deron Williams should they lose Williams to Dallas, but also a potential backcourt mate for Williams, who the Nets are scheduled to meet with Monday afternoon.
It has been widely anticipated that Phoenix would offer him a new two-year deal worth at least $20 million, but it remains to be seen how far Suns owner Robert Sarver will go when the bids start coming in.
The Arizona Republic reported Friday night that the Suns "do not appear willing to meet (Nash's) wish for a three-year deal" and Suns officials are already fighting the perception that they selected North Carolina point guard Kendall Marshall with the 13th pick in Thursday night's draft as the first step in dealing with Nash's eventual departure.
Nash earned nearly $12 million last season and averaged 12.5 points and 10.7 assists for a team that, with no 20-point scorer, nearly snagged the last playoff spot in the West.
Nash was born in South Africa but is a Canadian citizen and was even hired in May as general manager of the Canadian men's basketball team.
The Suns are one of four teams -- along with the Lakers, Raptors and Knicks -- interested in pursuing veteran small forward Grant Hill, a league source told ESPN The Magazine's Ric Bucher. Hill recently flew to Germany to undergo the same platelet-enrichment treatment on his knee that Lakers guard Kobe Bryant credited for his rejuvenated knee last season.