Can is regarded as one of Jurgen Klopp's key men at Anfield, but the German international has less than a year remaining on his contract and is yet to show a willingness to pen a new deal.
Juventus and Bayern Munich have been linked with the 23-year-old in the past, while Can himself is said to be keen on a move to Manchester City, but it appears that another team have joined the race for the player's signature.
According to The Mirror, Dortmund are ready to offer Can a route back to the Bundesliga, where he has previously represented Bayer Leverkusen.
Dortmund face an uphill task to reclaim the league title this season, with Der BVB currently six points off the pace in the standings, but it has been claimed that Can has been identified as a top target.
Should Can not agree fresh terms with Liverpool during the closing six weeks of 2017, negotiations can begin with foreign clubs at the start of next year.