The MLS club are widely reported to be close to signing the 31-year-old, a former team-mate of Nelsen during his brief spell at White Hart Lane in 2012.
Defoe has started just three of Tottenham's 20 Premier League games this season and been utilised mainly as an impact player off the bench, although the England international has netted seven goals in five UEFA Europa League games.
Despite his slump in fortunes, Nelsen claims Defoe remains in demand and has hinted that Toronto face late competition from some of the Premier League's leading sides to land the forward.
Nelsen told Sky Sports News: "I think if you ask any Premier League club then they would take Jermain right now.
"I know Tottenham are getting offers everywhere for him - for his services at the moment - and from top-four clubs in England at the moment as well.
"I know Jermain, I know his ability, I know his character so if we could get a player like Jermain that would be absolutely incredible but there are a lot of things in the air - there is nothing that has been done yet - he is not our player at the moment.
"We are working really hard and all I can say is if a quality player like Jermain Defoe graces the MLS it will be an amazing coup for the league."
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