Keita's future is up in the air at Lazio after he was left out of their squad for Sunday's Super Cup tie with Juve.
The Senegal international was hoping to play his part and tweeted that he was "profoundly hurt" to be left out of the squad.
Reports claim that Juventus had a 15million euros bid rejected but Spurs are willing to meet the 20million euros asking price.
Spurs boss Mauricio Pochettino is on the lookout for competition for Harry Kane, with Victor Janssen struggling to find his feet since his move last summer.
Monaco are also planning to a make a bid in the coming weeks but Spurs are confident the lure of the Premier League will be too much.