The Brazilian attacking midfielder is understood to be desperate to leave Ukraine amid the political trouble in the region, which has alerted Arsene Wenger.
Juan Fernando Quintero of Porto was thought o be the Frenchman’s top target, but with a deal seemingly out of the question he has switched his crosshairs back onto Costa – whom he is said to have been watching for some time.
Arsenal have already spent heavily this summer to land Alexis Sanchez, Callum Chambers, David Ospina and Mathieu Debuchy, but the 23-year-old South American is set to be a temporary signing with a view to a permanent deal.
However he will command a significant loan fee, with Shakhtar reluctant to let him go.
Costa has also been linked with Manchester United, but a switch to the Emirates Stadium is reportedly more appealing to him given their Champions League status and London location.