Nash was introduced to the White Hart Lane crowd before the 4-0 victory over Derby in August, at which he sat behind Levy in the directors' box. While he was there he discussed becoming involved with the club financially.
Nash, who plays for the Phoenix Suns and was named the league's best player in two of the last three seasons, told the New York Times: "I'd like to be an owner. It's something I could do for the rest of my life after my little window of popularity dies."
The 33-year-old is a lifelong Tottenham fan who has spoken of his joy at being allowed access to team training two summers ago. "Watching Spurs train was a complete dream come true for me," he said. "It was an excellent day and something I will never forget."
A close friend of Owen Hargreaves, Thierry Henry and Steve McManaman, Nash was born in South Africa but moved to Canada at the age of 18 months.
His father, John, was born in Tottenham and played professional football in South Africa, and Nash grew up playing football as much as basketball. His school team won the provincial championship and he was voted the best young player in British Columbia.
He has also trained with Major League Soccer's New York Red Bulls, and his brother, Martin, has won 33 caps for Canada and played for Stockport County, Chester City and Macclesfield Town.