Keita seems set to depart Lazio before the transfer window slams shut after he was omitted from their squad for Sunday's Super Cup clash with Juve.
The Senegal international had expected to be involved and voiced his displeasure at missing out on Twitter, saying he was "profoundly hurt" to be left out of the squad.
Keita is due to fall out of contract next summer and Juve are understood to have seen a 15million euros bid knocked back, with Lazio holding out for at least 20m euros.
Now reports indicate Premier League side Spurs and French champions Monaco are readying rival moves and Juve will have to up their offer to seal a deal.
Keita's preference is understood to be a switch to Juventus but the Serie A champions face the prospect of missing out if they do not match Lazio's valuation.