The newspaper claims that Trabzonspor have been keeping close tabs on the Nigerian international but are yet to make a formal offer.
Brown joined West Brom on a £10 million move from Dynamo Moscow and still has two years left on his current contract.
The Nigerian international became the Baggies record signing last summer but struggled to settle in.
The 26-year-old striker scored a total of four goals in 24 games in all competitions for the Premier League outfit last season.
Trabzonspor have been targeting an additional striker to partner Paraguayan international Oscar Cardozo next season.
The Black Sea Storm are planning to add depth and strengthen their attacking line to cope with the Europa League and league campaign fixture list.
The Super Lig outfit finished last season in fifth place and are currently coached by Shota Arveladze who replaced Ersun Yanal last month.