Keita's representative Roberto Calenda said on Thursday that he had been informed a deal had been reached with the Rossoneri, adding there was never "a concrete offer of a renewal".
Lazio sporting director Igli Tare insists that is not the case, stating the 22-year-old was offered an extension that would have put him among the club's best-paid players.
However, Tare failed to address Calenda's comments about a move to Milan having been agreed, suggesting a switch to San Siro is on the horizon.
"I take note of the comments by Mr Roberto Calenda, who says he never received any official offer to renew with his client Keita Balde Diao. Such statements do not reflect reality," Tare said in a statement.
"No more than two weeks ago there was yet another meeting with him. His client was offered an official contract both last year and during the season that has just finished.
"I want to be very clear that the player was formally offered a contract renewal at the same figures as Lazio's top players."
Keita's move is reported to be part of a double deal worth €50million that will also see Lucas Biglia swap Lazio for Milan.
The former Barcelona youngster's contract is set to expire at the end of next season, which is believed to have prompted Lazio's decision to cash in.