The Reds boss is reportedly monitoring developments at the German club, as Huntelaar delayed talks over a new contract, prompting speculation he could be willing to listen to offers from elsewhere.
The Dutch international's current deal expires at the end of the season, allowing him to negotiate a pre-contract agreement with another club from January onwards.
If he fails to sign a new deal with Schalke, the Bundesliga club could be tempted to cut their losses and sell the frontman, rather than risk losing him for free next summer.
And Liverpool boss Rodgers is reportedly keen to take advantage of such a scenario by putting together a cut-price package for the Holland international.
The Anfield club are struggling up front, with only one fit senior striker. Fabio Borini, a summer signing from AS Roma, has been ruled out for up to three months with a fractured foot, leaving Luis Suarez as the Reds' sole striker.
The Reds could call on youth team duo Adam Morgan and Samed Yesil, and Liverpool have blooded several youngsters this term, but Rodgers is thought to want more strength in depth up front.
The Daily Mail reports Manchester United, Arsenal and Tottenham are also interested in Huntelaar, but Liverpool have by far the greatest need for a forward.
The Reds secured their first home win of the Brendan Rodgers' era in the Premier League on Saturday, beating Reading 1-0 at Anfield thanks to a goal from 17-year-old Raheem Sterling.
But Liverpool again struggled to find a cutting edge, with Suarez occupying the lone striker role.