Welsh midfielder Ramsey is in the last year of his Gunners contract and they are ready to sell to finance their own transfer ambitions.
Chelsea boss Maurizio Sarri has accepted defeat in his interest in Aston Villa’s Jack Grealish, who will head to Tottenham – if he can persuade Villa to sell him – so he can play in the Champions League.
Sarri, who has missed out on several Italian targets, will turn to Ramsey, who is yet to sign a new deal at Arsenal.
Henrikh Mkhitaryan, who joined Ramsey at Arsenal in January, is hoping his team-mate sticks with the Gunners beyond the summer.
“His work rate is very, very high and everyone appreciates what he does on the pitch and off it, because he’s a true professional,” said Mkhitaryan.
“Of course it’s very easy to play next to him because he tries to be everywhere to help the team – to score goals, to assist, to tackle, recover balls – and that’s why I’m going to be very happy if he stays at the club.
“I think he’s been with the club for 10 years already and it seems that he became a symbol for this club.
“I will be very happy for him if he signs a new contract because he’s in the history of Arsenal already and I hope he can become a legend for Arsenal after a few more years.”
Former Premier League star Dean Ashton believes the midfielder would represent a huge loss if he was to quit the Emirates.
“Aaron Ramsey’s stats from last season are impressive,” said Ashton.
“He got one more assist and three more goals than Mesut Ozil. He goes under the radar.
“Arsenal would be surprised how much they’d miss him – he influences games and it’s strange they haven’t signed up on a new deal.”