Naby Keita could become a earlier than expected if the Anfield club decide to pay up an additional £13 million.
The Reds have an agreement in place for the Guinea worldwide to join them in July, having paid a premium to secure his services before a £48million buy-out became active in the summer.
With Philippe Coutinho's move to Barcelona, RB Leipzig had appeared even more adamant in their stance that Keita would not be allowed to leave in January as they are now challenging for Champions League qualification and are preparing for the Europa League knockout stages.
Liverpool hierarchy have approached Leipzig about securing a deal that could get the player to Merseyside this month. The 22-year-old Keita has not been able to reproduce the same form this season that captured Liverpool's attention and subsequent signing of the player.
The arrival of Keita would go some way in remedying that.
More than anything else, bringing the Keita deal forward would appease fans anxious allowing Coutinho to leave halfway through the season could disrupt the quest for a top-four spot and progression deep into the Champions League.