Sky Bet are offering odds of just 6/1 that the German will be at Anfield at the end of the January transfer window.
Barcelona (12/1) remain in the hunt, while Manchester United (20/1) are also understood to be interested along with Real Madrid (also 20/1).
Liverpool were said to be lining up an offer under former manager Brendan Rodgers but a deal failed to materialise over the summer.
And they may have a better chance of getting him now Jurgen Klopp has taken the reins.
GETTY
Liverpool are the favourites to secure signing of Marco Reus
Reus, 24, worked with Klopp at Dortmund for three seasons before the boss departed the Westfalenstadion at the end of the last campaign.
Together they won two Bundesliga titles and reached the final of the Champions League.
Klopp has already said he won't raid his former club for their stars but previous reports claim Reus could be keen to link up with his ex-manager again.
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy