Riyad Mahrez has handed in an official transfer request at Leicester while Manchester City have made a third bid, thought to be £55m, for the player, Sky Sports News understands.
The transfer, if successful, would put Mahrez second amongst City's most expensive purchases, behind new arrival Aymeric Laporte.
Mahrez would be by far Leicester's most expensive export, dwarfing the £35m they received for Danny Drinkwater from Chelsea.
Earlier on Tuesday, Sky Sports News reported that a bid, which was believed to be City's second for the Algeria international in this window, was well below the Foxes' valuation of the player, who also handed in a transfer request in May 2017.
Following news of a third bid, we understand that Leicester's position remains the same. They say they are yet to receive a "formal bid" but discussions over money are still happening this evening.
Leicester are still adamant they do not want to sell the player and that City's offer remains well below their valuation.
Nevertheless, Mahrez did not go to the Leicester City training ground on Friday and has not travelled with the rest of the squad to Merseyside ahead of their game against Everton.
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Speaking earlier this month, Foxes boss Claude Puel was asked if Mahrez could cost potential suitors £100m. He said: "Perhaps; maybe in the summer he will cost even more than £100m. [But] it's just rumours, noise about him. We can see Riyad smile, enjoying his football, enjoying to play with his team-mates."
Mahrez wanted to leave last summer and submitted a transfer request amid interest from Roma, but the Foxes refused to sell the 26-year-old after rejecting three bids from the Italian club - including a £31.8m offer.
Speaking at the time, Mahrez said: "Out of the huge admiration and respect I hold for Leicester City, I wanted to be totally honest and transparent with them and have therefore informed the club that I feel now is the time for me to move on.
"I had a good discussion with the chairman last summer and we agreed at that time that I would stay for another year in order to help the club as best as I could following the transition of winning the title and in the Champions League.
"However, I am fiercely ambitious and feel that now is the time to move on to a new experience."
City have submitted their second bid for Mahrez after confirming Leroy Sane suffered ankle ligament damage during Sunday's FA Cup fourth-round win over Cardiff.
Sane has been ruled out for up to six weeks and is set to miss the Carabao Cup final against Arsenal as well as both legs of City's Champions League last-16 tie against Basel.