The former Lille man has struggled to become a regular starter for the Foxes over the likes of Youri Tielemans, Wilfred Ndidi and Kiernan Dewsbury-Hall and is being strongly linked with an exit.
Leicester can afford to drive a hard bargain with Soumare under contract until 2026, and Monaco are already believed to have seen a bid of £15m rejected.
Now, the Daily Mail claims that Les Monegasques have come back with an improved bid for the 23-year-old, as Leicester hold out for a £23m fee to recoup the entirety of the money they shelled out to sign him from Lille last year.
Soumare helped Lille win the Ligue 1 title in the 2020-21 season but is yet to play a single minute of Premier League football for Leicester in the 2022-23 campaign.
Soumare is not the only Leicester player whose future is being called into question, as speculation continues to swirl surrounding Youri Tielemans's next career move.
The Belgium international has now entered the final year of his contract at the King Power and is still being linked with a move to Arsenal, whom he featured against in Saturday's 4-2 defeat.
However, the Gunners are supposedly ready to wait until next year to try to sign the former Monaco man, with Leicester demanding in excess of £30m to sanction a sale this summer.
According to The Times, Leicester are hoping to retain Tielemans's services for the 2022-23 season but have resigned themselves to losing him on a free transfer at the end of the campaign.
The 25-year-old is also believed to have attracted the attention of Manchester United after coming up with 24 goals and 24 assists in 160 games for Leicester since January 2019.
Over at the City Ground, Nottingham Forest's non-stop summer business is showing no signs of slowing down anytime soon as Steve Cooper seeks more reinforcements in attack.
The Tricky Trees have already added to their forward line with the signings of Taiwo Awoniyi and Emmanuel Dennis, but more strikers could still come through the door.
According to L'Equipe, Forest have tabled an upfront bid of €4m (£3.4m) for Bordeaux striker Hwang Ui-jo, which could total €5m (£4.2m) with performance-related add-ons.
The report adds that the Ligue 2 side are prepared to accept the offer for the South Korea international, who hit double figures in the 2020-21 and 2021-22 Ligue 1 campaigns.
However, Hwang's 11 goals last year could not prevent Les Girondins from suffering a devastating relegation to Ligue 2, but they managed to avoid a further demotion.
Elsewhere in France, Ander Herrera is seemingly set to become a victim of Christophe Galtier's major midfield overhaul at Paris Saint-Germain following the arrivals of Vitinha and Renato Sanches.
With Fabian Ruiz also set to join from Napoli, Herrera's opportunities for starts will become increasingly limited, and the 33-year-old is out of contract at the Parc des Princes in 2024.
Herrera represented Athletic Bilbao between 2011 and 2014 before earning a big-money move to Manchester United, and L'Equipe claims that the Spaniard is pining for a return to his homeland.
Herrera has supposedly been training with the reserves as PSG try to negotiate a contract termination with the midfielder, and the financial aspects of such an eventuality are yet to be agreed.
The former Man United man provided three goals and two assists in 19 Ligue 1 games last term and is believed to earn a weekly wage of €150,000 (£126,800) at the Parc des Princes.