Current club captain Mertesacker is set to retire at the end of the 2017/18 season and Wenger revealed this week that Ramsey is a potential candidate to replace the German World Cup winner.
Ramsey did captain Wales in 2012, but after the shock death of his predecessor Gary Speed, Coleman relieved him of the armband in order to take some pressure off his shoulders.
'I tried to take the pressure off him because a lot of things had changed,' Coleman said.
'So I went to Arsenal's training ground to talk to him and he was brilliant.
'He could have spat his dummy out because he is a great player for us, but he was absolutely fantastic.
'He accepted it and I'm not surprised by Arsene's comments about him being a future Arsenal captain.'
Wales will now start preparing for their crunch 2018 World Cup qualifiers against Georgia and the Republic of Ireland, and Coleman says he expects Ramsey to captain Wales once more.
'Whether I am a manager or not I see him as the Wales captain again in the future,' Coleman said.
'I told him that when I took the captaincy off him because he's got that about him.
'Mind you, he's in good company with Gareth Bale and Chris Gunter with his experience.
'He's not had an easy ride at Arsenal, he's had a lot of criticism and it's the same with Gareth (Bale) at (Real) Madrid.
'Aaron has come out with his sleeves rolled up and thought 'I am going to show those who doubt me'. He keeps on doing that again and again.'
Do you think Ramsey has the credentials to take on the role as Arsenal captain?