The 34-year-old’s deal with the Premier League side expired on June 30 and he is currently a free agent.
The Evening Standard reports that Spurs are prepared to hand the Spaniard a new one-year deal on reduced terms from his previous £100,000-per-week contract.
Llorente will now consider his next move as he weighs up his options, which include Fiorentina and a possible switch back to Spain.
The former Swansea striker scored just one goal in 20 Premier League appearances for Mauricio Pochettino's side last season, but chipped in with crucial strikes against Borussia Dortmund and Manchester City during their run to the Champions League final.
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