The Reds wanted to sign the Frenchman last summer but he snubbed them in favour of joining Real Madrid.
His first season in the Spanish capital did not go according to plan as the midfielder struggled to establish himself in the starting eleven.
There have been talk of him leaving the club this summer with Liverpool getting in contact with him again early in the transfer window.
But both Real Madrid and Tchouameni are clear about continuing their association and according to Spanish outlet Relevo, there has been no recent contract from the Reds.
The 23-year-old midfielder is keen to continue at Real Madrid and even the Spanish giants do not want to give up on him after just one season.
The Merseyside giants are having their own struggles to sign a defensive midfielder but they have not gone back for Tchouameni.
Liverpool have lost out on signing Moises Caicedo to Chelsea and the Blues are also pushing to hijack their pursuit of Romeo Lavia.
