Ramsey scored twice for Arsenal as they strolled to a 4-1 win over CSKA Moscow in the first leg of their Europa League quarter-finals on Thursday.
"Yes, I'm confident, he's not at the end of his contract, he has one and a half years to go. From my side it is clear, but you always have to find an agreement," Wenger told reporters on Friday.
"We want him to stay. He's one of these guys who has been here for a long time. He will be an important player in the future of this club."
Wenger said he will not convince Ramsey to sign a new deal if the Wales international is hesitant as he wants all his players to be grateful to play for the north London club.
"I don't want to convince a player (they should sign)," Wenger added. "I want the player to be happy to play for the club.
"Having players who want to play for the club is the way we want to play football and is in the values we feel are important to us."
Arsenal are sixth in the league table and host relegation-threatened Southampton on Sunday.
(Reporting by Aditi Prakash in Bengaluru)
