The 21-year-old Russian has made a strong impression since joining from Lokomotiv Moscow in the summer, attracting rave reviews and prompting an increase in scouting activity around him.
His next Champions League appearance against Aston Villa is expected to draw significant attention from clubs across Europe, with several scouts planning to assess how he performs against Premier League opposition.
Batrakov's rapid development has caught the eye of some of the biggest sides in the game, and there is a growing belief that his time in Turkey could be relatively short.
Arsenal, Tottenham, Liverpool and Manchester United are among the admirers. Paris Saint-Germain and Barcelona have also been linked.
Despite having limited experience at the highest level, his performances have convinced influential figures in the game that he has the talent to make the step up.
Galatasaray would naturally prefer to keep hold of a player who has quickly become popular with supporters, and want to tie him to an improved deal. However, the scale of the interest means they could face a difficult task retaining him if leading clubs decide to make their move.
Batrakov is believed to be available for around £50 million at the end of the season. His age, technical qualities and potential for further development make him an appealing proposition, particularly given how quickly he has adapted to a new environment.
The upcoming November 24th Aston Villa fixture could prove another important reference point in that process.
Performing against Premier League opposition would offer scouts a useful indication of how his qualities translate against a different level and style of competition.