Jurgen Klopp is keen to bring in defensive reinforcements this summer.
Liverpool have been heavily linked with Southampton star Virgil van Dijk in recent months.
However, the Reds pulled out of the race for the Dutch defender after tapping up allegations.
Van Dijk, who handed in a transfer request earlier this month, is still keen to move to Liverpool and work with Klopp at Anfield.
However, German outlet DW Sports say Klopp is eyeing a move for Schalke defender Howedes.
They reckon Liverpool are willing to spend £18m (€20m) on the Germany international.
DW Sports tweeted: “Jurgen Klopp is interested in bringing former Schalke captain Benedikt Howedes to the Premier League for €20m.”
Van Dijk is yet to play for the Saints this season after handing in his transfer request.
Liverpool, Chelsea and Manchester City are said to be chasing the former Celtic star, 26.
The Reds have had a hit-and-miss start to the season, picking up four points from their opening two Premier League games.
