The report goes onto claim that Inter, Atletico Madrid, Valencia and West Ham are also closely monitoring the Turkish international.
Töre has been in impressive form for the Black Eagles providing five assists and netting once in six league games this season.
The 23-year-old is no stranger to the Premier League having risen through the youth ranks at Chelsea before joining HSV, Rubin Kazan and finally Beşiktaş.
The explosive winger had an impressive run in the Bundesliga, struggled to settle in Russia but found his feet again under current Hammers boss Slaven Bilic scoring nine times and providing 11 assists in all competitions last season.
Whoscored rate Töre as currently being statistically the sixth best player in the Turkish Super League.
Beşiktaş received as offer from Atletico Madrid over the summer but underlined that they would not sell their star man for under their €20 million valuation.
Töre has been called up to the Turkish national team side that will face the Czech Republic and Iceland in the last Euro 2016 Group A qualifiers.