Ramsey, who Wenger brought to the club way back in 2008, is out of contract at the end of the season and is expected to move on for pastures new
The likes of Manchester United, Chelsea and Juventus have all been linked with the Welshman, who has already revealed his intention to remain with Arsenal until his contract expires in the hope the two parties can come to an agreement to extend his decade-long association with the club.
Now, Wenger has had his say, insisting that there is every chance the 27-year-old could yet commit his long-term future to the club.
"We tried that before and it still can happen," Wenger said of handing Ramsey a new deal.
"I don't really know what is happening at Arsenal. Sure, Aaron Ramsey is in a strong position now and he will use this position.
"But I don't know how far Arsenal will go in terms of giving him a huge contract. These things were once my responsibility but not anymore. I am happy about that."