Suarez has consistently blamed intrusion from the English media for his wish to leave Liverpool this summer, and Real Madrid remain favourites for his signature with Sky Bet.
Arsenal have already had one offer for the striker rebuffed but, amid reports a new bid is being prepared, Sky sources understand he has not ruled out joining an English club in the Champions League.
The healthy relationship between the two clubs' boards is of further encouragement to the Londoners and, when asked whether there was a genuine possibility Suarez might start next season at Arsenal, a source close to the negotiations said: "Maybe."
Arsene Wenger, meanwhile, would not be drawn on specific targets as he arrived in Vietnam for the latest leg of his side's pre-season tour.
Wenger said: "You want me to announce a spectacular signing, but I can't. We are working behind the scenes to strengthen the squad - but I can't give you names."
Wenger will send out a team to face Vietnam in Hanoi on Wednesday on the back of a 7-0 victory over an Indonesia Dream Team at the weekend.
The Frenchman has been also been linked with moves for Real Madrid's Gonzalo Higuain and Manchester United's Wayne Rooney, and he last week described those two players - and Suarez - as "realistic targets, quality-wise."