The South Korea international left-back is keen on a move to Italy and almost joined Roma last summer.
Spurs boss Martin Jol is expected to sell one of his left-backs this close-season following the arrival of £10 million teenager Gareth Bale and Lee is mooted as a prime candidate.
Roma remain keen on the ex-PSV man, while Torino president Urbano Cairo is also anxious to lift his club's profile in the Far East.