Keita scored 16 goals last season and the 22-year-old is seen as one of world football's brightest young talents.
The Mirror report Spurs are battling Juventus for his signature, and his future is unclear after he was omitted from the club's Italian Super Cup squad on Sunday.
A war of words has since ensued, with Keita's agent blaming Lazio for being unwilling to invest in him.
He said: "In these two days we read about everything. I categorically deny that Keita has pulled out or had muscular problems (as he himself, however, clarified after knowing the exclusion).
"In fact, he always trained with commitment, getting ready for the game as usual (and his preparations all know him, since last year he played sculls of matches, he scored 16 goals).
"The truth is in the eyes of everyone: Keita did not bid for a proper contract renewal and [Lazio] did not convene him for the first major game of the season.
"I did not say he would not play: he was not even summoned. Obviously the club does not intend to invest in the player. The rest are chatting and they only serve to mask this reality."
Lazio have feared Keita is trying to push a move to Juventus, but The Mirror report they are determined not to sell to Italian champions.
As the situation unravels and the war of words escalates, the better it is for Tottenham's hopes of convincing the player to join and lead their attack along with two-time golden boot winner Harry Kane.