The 22-year-old France international could be sold in the current transfer window, with Arsenal and the Reds both keen on acquiring his services.
Monaco head coach Leonardo Jardim accepts he may be unable to keep Thomas Lemar at the club during the January transfer window.
Vice-president Vadim Vasilyev and Jardim have previously been clear that Lemar and other Monaco stars including Fabinho will not be allowed to leave mid-season.
Kylian Mbappe, Bernardo Silva and Benjamin Mendy departed last season’s Ligue 1 champions, who sit second in the table, nine points behind Mbappe’s new side Paris Saint-Germain.
Lemar reportedly was close to joining Arsenal on deadline day only for the move to fall through, scuppering Alexis Sanchez’s planned switch to Manchester City in the process.
The versatile France international has also been linked with Liverpool, who are seeking replacements for key midfielder Philippe Coutinho after he sealed a dream move to Barcelona.
Jardim stressed again that Monaco do not typically sell players in the January transfer window, but the coach understands a large bid for Lemar would give his side a decision to make.
“We are not used to selling in the winter,” Jardim told reporters on Monday.
“But the transfer window lasts until the end of the month and many things can happen.”
Jardim suggested fringe players could be allowed to follow Terence Kongolo and Soualiho Meite by leaving Monaco on loan.
“Maybe a few who play little will be able to find time for play,” Jardim added.
Lemar has been included in Monaco’s squad for Tuesday’s Coupe de la Ligue quarter-final at Nice, but striker Radamel Falcao is out with a calf injury.