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Lo Celso has been on superb form this season, registering nine goals and four assists in 32 LaLiga matches.
The Argentine currently has a €100m (£88m) release clause and it is understood Betis want to sell him for a fee closer to that amount.
North London deal-makers will also have to fend off interest to land the playmaker, who is also attracting interest from other Premier League clubs.
Spurs have not signed a player since Lucas Moura was signed for £23m from Paris-Saint Germain in January 2018.
Their previous record signing was completed in August 2017 when defender Davinson Sanchez arrived from Ajax for £42m.