AS says the two Premier League clubs are considering Bade for this month's transfer window.
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It's been suggested Sevilla would be willing to sell for €25-30m.
The centre-back's contract with Sevilla extends until the summer of 2029.
A move to Liverpool or Newcastle would mark a Premier League return for Bade, who had a spell on-loan at Nottingham Forest from Rennes in 2023.