The manager asked the player to leave if he wants because it would be difficult for him to play first team football this season.
Welbeck has entered the final year of his contract at the Emirates but has fallen further down the pecking order since the arrival of Pierre-Emerick Aubameyang.
The England international has suffered series of injuries since joining the Gunners from Manchester United in 2014 and has failed to start in over 50% of his league matches in each of his four campaigns at the club.
The Times, UK, reports that the Gunners are ready to cash in this summer and will consider offers from interested party, Everton.
The new Arsenal boss has completed six signings so far this summer but is open to making another as the transfer window enters its final week.