The Gunners could add to their options in the final third when they look at the transfer market this summer.
Last year’s Ukrainian league runners-up are reportedly looking to get rid of the pair, alerting the attention of north London giants Arsenal.
The 28-year-old Taison has featured in just 16 league matches this term and has found the net on six occasions.
The former Metalist Kharkiv winger joined Shakhtar in January 2013 for a fee of around £12 million and scored his first Champions League in October that year in a 1-1 draw against Manchester United.
His compatriot Wellington Nem, meanwhile, has been forced to watch on from the sidelines this season with the 24-year-old featuring in just six league games to date.
The left-footed attacker has been used sparingly since his €9 million move from Fluminense in July 2013, clocking up a total of just 19 games.
Arsenal boss Wenger will no doubt be eager to add to his striker department in the off-season to help ease the goal scoring burden on France international Olivier Giroud, with Theo Walcott failing to persuade his manager he is a suitable back-up in a central role.