The Armenian midfielder believes the 27-year-old has what it takes to become a club legend at the Emirates.
Ramsey has less than a year remaining on his current contract with the Gunners and he is yet to renew his deal.
Speaking about Ramsey’s future, Mkhitaryan said: “I think he has already been at this club for 10 years if I am not wrong.
“And it seems that he became a symbol for this club and I will be very happy for him if he is going to sign a new contract because he has a history of Arsenal already.
“And I hope he can become a legend for Arsenal after a few years.”
Ramsey confirmed earlier this week that his agent is in talks with the Gunners over a new contract.
He said: “Talks are still ongoing. I’ve got nothing else to say about that.
“We’ll see what happens, my agent and the club are talking.”
When asked what he decision relies on, the Welshman added: “I’m not sure exactly.
“I’m leaving that to them to discuss and figure out.
“But we have come to an agreement, that’s something that my agent and the club are discussing to try to get something done.”
Ramsey has been with the Gunners since 2008 after he joined from Cardiff City for £4.8million.
If he does not pen a new deal in North London, Arsenal will be at risk of losing him for free in 12 months.