Everton and Chelsea are also reportedly interested in the Ukraine star.
The Gunners completed their first signing of the January transfer window this week, as midfielder Mohamed Elneny finalised his protracted move from FC Basel.
Manager Arsene Wenger could now look to add more to his squad though in an attempt to provide a boost to their Premier League title challenge this season.
And among his targets could be Ukrainian winger Yarmolenko, with the Gunners reportedly having made an enquiry for the star.
They are not the only club in the Premier League with an interest in his services though, with Chelsea and Everton also making enquiries for his services.
Kyiv are not keen on losing their star man though, and have set an asking price of €27million for him, around £20million, according to the Mundo Deportivo report.
Yarmolenko is a key player for the Ukrainian side and his country, and they would likely prefer to wait until after Euro 2016, as a good tournament could see both interest in him and his price soar.