The Germany star has reportedly been told by Paris St-Germain that he can leave the club.
And with Liverpool looking to strengthen and Jurgen Klopp in charge, the Reds are at 11/8 to sign Draxler.
Arsenal are second favourites at 9/2 with Barcelona at 8/1.
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BetStars Director of Trading Ian Marmion explained: "Liverpool have emerged as the clear 11/8 favourites to sign PSG"s Julian Draxler, after being told he is no longer needed at the Parc des Princes.
"The World Cup winner only joined the Paris side in January but since the arrival of Brazilian star Neymar, Draxler has become surplus to requirements.
"The German international will be the creative influence that Liverpool need should they sell Coutinho to Barcelona.
"Arsenal are second in the running for Draxler and are priced at 9/2 to sign the skilful midfielder, with Barcelona making up the betting at 8/1.”
Draxler has had an impressive summer helping Germany to glory in the Confederations Cup.
The 23-year-old will be a man in demand if the reports are accurate with Premier League rivals likely to vie for his signature.
Liverpool are looking to add depth to their squad as they prepare for a return to the Champions League.
And with Philippe Coutinho said to be closing in on a switch to Barcelona, Draxler could be a good replacement.
