Rosler has revealed that the club has held talks with Watson's agent, but that they have not yet came to an agreement with the midfielder.
However, the German did admit that as far as he was aware, the 28-year-old former Crystal Palace midfielder would like to stay at the Lancashire outfit.
Watson scored the winning goal in last season's FA Cup final against Manchester City at Wembley, and Rosler has made it clear that the club will offer him the best deal they can, albeit within their means.
The Latics manager said that as soon as he met with Watson, he was adamant that he wanted to continue working with him after his contract expires in the summer.
Speaking to the Wigan Evening Post, Rosler stated: "We've had talks with Ben's agent over a new contract, but we're not there so far. I did get the impression he'd like to stay and we would certainly like him to stay.
"We will make Ben an attractive offer, but there is a limit. He's at a good age in terms of the fact he's got some good years in front of him.
"Within 10 days, I said I wanted to continue working with him. So it's up to him now."
The German then added: "It's unfortunate that a player of this stature is so close to the end of his contract, but it happened before I came."