Cherki faces an uncertain future in France after Lyon were recently told they will be relegated unless they bring their finances under control.
The Direction Nationale du Controle de Gestion (DNCG) handed the provisional relegation to Lyon, who have racked up nearly £500m in debts.
As a result, the Ligue 1 side will likely need to raise funds through player sales to help improve their perilous financial situation.
Cherki is one of those who has been linked with a move away despite only signing a new contract until 2026 back in the summer.
Liverpool submit Cherki bid but face Chelsea competition
Liverpool are among Cherki's potential suitors, and they recently made an enquiry over the Frenchman's potential availability.
According to TuttoJuve, Liverpool have stepped up their interest by tabling a €20m (£17m) bid to sign the Lyon attacker in 2025.
While it remains to be seen whether Lyon will accept the proposal, Liverpool will have to fend off competition from Chelsea if they are to have any hope of landing Cherki.
The report claims that Chelsea have joined Liverpool submitting a €20m (£17m) offer, raising the prospect of a transfer battle between the two clubs ahead of the January window.
Outside of the Premier League, Italian giants Juventus are also said to be an admirer of the France Under-21 international.
Will Lyon sell Cherki in January?
Lyon will be keen to keep Cherki for the remainder of the season, but have to consider January offers due to their financial situation.
However, Lyon president John Textor recently fired a warning that he is not planning to allow Cherki to leave the club on the cheap.
"We lost €15m (£12.5m) from his potential sale [to Paris Saint-Germain] last summer, but now his value is way higher," Textor said via 90min. "He should stay in January, but it's up to Rayan, as is always the case in football."
The Lyon academy product has racked up 152 competitive appearances for the senior side, scoring 19 goals and providing 28 assists in all competitions.
The 21-year-old is a versatile attacker, having previously demonstrated his ability to play as an attacking midfielder and on the flanks.