Mykhailo Mudryk could make his Arsenal debut against Manchester United next weekend.
The Gunners remain confident of completing a deal worth £80m for the player.
The Premier League leaders submitted their third bid for the Ukraine international on Thursday as they look to beat London rivals Chelsea to a deal.
While the finer points of the transfer still need to be agreed, there is an acceptance from all parties that the deal will be completed soon, according to The Times.
Arsenal wanted to pay around £50m upfront but Shakhtar Donetsk are looking for more and want the add-ons included to be realistic.
Such has been the progress in talks between Arsenal and Shakhtar, the Gunners are reportedly confident that Mudryk will be available for the club’s Premier League clash against Man United on January 22.
It is claimed the bonus clauses are expected to include Arsenal winning the Premier League – they are currently five points clear at the top of the table – and qualifying for the Champions League.
Mudryk, who has scored 10 goals this season, is currently with his Shakhtar Donetsk team-mates at a training camp in Turkey.
The 22-year-old has not hidden his desire to join Arsenal and recently posted a picture on Instagram in which he was wearing the club’s shirt.
Asked if he had been following Mudryk’s social media activity, Arsenal boss Mikel Arteta said on Friday: ‘What I would say is how good I am with the phone. You know we cannot talk about any other players.
‘There is some interest on some things that we would like to do to improve the team because we are a bit short in certain areas and with injuries that we picked up.
‘But we are trying as a club we are determined to try and improve the team in every window and that’ what we are trying to do.’