Wales are playing in their first major tournament for 50 years after a tremendous qualifying campaign spearheaded by Gareth Bale and Ramsey.
Ramsey said that Wenger felt they could be a threat in France also.
“The manager, Wenger was pleased for me that we qualified,” said Ramsey.
“He said we could be pretty dangerous over there so hopefully that proves to be right. He’s a wise man.”
Ramsey also spoke of the banter exchanged by his England teammates and him. Gareth Bale took aim at England’s assessment of themselves.
“Normally I’m on holiday now,” Ramsey said.
“When the campaign started and we got those couple of wins early on I kept winding the Arsenal boys up saying ‘I’ll see you in France’.
“The way things were developing it was looking promising. To finally achieve it was great.
“To go in knowing I would actually be playing in the finals, I can share that experience now with some of the players who’ve done it.
“I know what it’s like with other sports in the country, in the Six Nations the whole nation is there for you.
“I wouldn’t say I was jealous of rugby, but I wanted to experience that same buzz they get from the block where that’s all people talk about.”