The 21-year-old defender - who currently plies his trade with Valenciennes - is fast becoming one of the most highly rated youngsters in Ligue 1, and as a result has attracted attention from a number of different clubs.
Reds boss Brendan Rodgers has been credited with an interest in bringing the player to Anfield this month, as speculation continues to surround the future of Sebastian Coates on Merseyside.
Coates endured a nightmare 90 minutes during Liverpool's shock 3-2 defeat to Oldham Athletic in the FA Cup fourth round on Sunday, fuelling rumours he could be dumped by the Premier League outfit before the close of the transfer window.
That will likely depend on whether or not Rodgers can find a suitable replacement, as he looks to add competition for centre-back places, with Daniel Agger and Martin Skrtel comfortably Liverpool's first-choice options at the moment.
Isimat-Mirin has established himself as a key figure in the Valenciennes first-team since making his debut in 2010, with his impressive form also earning him a call-up to France's U21 side.
A graduate of the Clairefontaine academy, the player's recent performances haven't gone unnoticed, and Lille have already approached Valenciennes about the possibility of a transfer.
The French club are yet to agree a fee with their domestic rivals, though, which could allow Liverpool to hijack the move, if they wish to make a last-ditch attempt to sign the defender.
Earlier this month, the Daily Star linked Newcastle United with a move for Isimat-Mirin, who is rated at around £5million.
However, after completing the signing of Mapou Yanga-Mbiwa from Montpellier, Alan Pardew's interest in the centre-back now looks to have waned.