Liverpool have money to spend following Philippe Coutinho’s £142million move to Barcelona earlier this month.
Riyad Mahrez emerged as a surprise candidate to come in as Coutinho’s replacement while Liverpool are looking at the possibility of bringing forward Naby Keita’s move to Anfield.
But Monaco winger Lemar has consistently been linked with a move to Liverpool after they made an approach in the summer.
Arsenal are also interested in a move for the France international and came close to signing him at the start of the season only for a deal to fall through.
Monaco have left the door open for Lemar to leave this month.
And the Sunday Times claim he remains Liverpool’s top priority to sign, although they could wait until the summer to make their move.
However, they have been unable to make a breakthrough in negotiations with Monaco who are unwilling to drop their £90m valuation.
Liverpool are said to be only prepared to pay close to £60m and if Monaco refuse to lower their asking price, Jurgen Klopp is prepared to look elsewhere.
And it is reported he could be tempted to raid his former club, Dortmund, to sign 19-year-old Politic.
The Bundesliga giants supposedly don’t want to sell the USA international until 2019 and Manchester United have also been touted as potential suitors.