The 23-year-old has blossomed into a star for Gala this season and recently impressed in the Europa League last-16 tie with Barcelona.
Akturkoglu, who has eight goals and five assists in 29 Super Lig outings, is now attracting interest from some of Europe's biggest clubs.
Turkish outlet Aksam has reported that both north London clubs will continue to scout the talented winger for the remainder of this season.
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