Wissa joined on deadline day last summer as a replacement for Alexander Isak, who moved to Liverpool in a British transfer record deal.
But the 29-year-old has managed just one goal in 14 Premier League appearances, with a serious knee injury sustained on international duty before he had even trained with his new teammates setting back his entire campaign.
Newcastle have not yet decided to sell, and head coach Eddie Howe has publicly backed Wissa, insisting he is now fit and training fully with the group.
A fee of around £15 million would represent a loss of roughly £35 million on the original outlay — one of the heaviest financial hits the club has taken in the Saudi-era transfer market.
The possible buyer has not been identified. Fenerbahçe have been named in earlier reports as one club monitoring his situation. Wissa still has three years remaining on his contract, which complicates any potential negotiations.
If a sale does materialise, it would represent part of a wider summer restructuring at St James' Park. Newcastle are also exploring the market for a new striker, which itself raises questions about Wissa's standing in Howe's plans for next season regardless of whether an acceptable offer arrives.