The England defender was sold by the Reds earlier this summer for €30m to Bayer.
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And the Liverpool Echo says as part of the deal a buy-back clause was inserted in the arrangement.
The Reds can re-sign Quansah in 2027 for a set price of €60m - and it's an option the Premier League champions are taking seriously.
In addition, Liverpool have already reached an agreement with Quansah on the personal terms of a possible return.