The Gunners have put a formal contract offer to Willian, who is expected to leave Chelsea at the end of his contract, and are claimed to be highly likely to complete the deal.
Arsenal were offered the chance to sign Coutinho from Barcelona, but are instead prioritising Willian.
If they complete the capture of Willian then, it is claimed, they will not sign Coutinho as they have no intention of signing both players.
Coutinho spent this season on loan at Bayern Munich in the Bundesliga and the Bavarians had an option to sign him permanently.
They did not trigger it and Barcelona are again looking to ship out the Brazilian midfielder.
A host of Premier League clubs have been linked with the former Liverpool man, but so far he is still at the Camp Nou.
If Arsenal can push the signing of Willian over the line then they will bow out of the chase for Coutinho and it remains to be seen where the midfielder will end up.
