The 30-year-old Welsh international has travelled to Reading for talks.
Edwards has found himself on the fringes of the first team this season, with his two starts coming in the Carabao Cup including in Wednesday evening's 2-0 win at Southampton.
The midfielder, who joined Wolves in January 2008, is contracted to the club until 2019 but Nuno Espirito Santo doesn't see him as playing a key role this season.
The Royals have already signed one Wolves player this summer after swooping for striker Jon Dadi Bodvarsson in a deal believed to be worth £3m.
Reports linking winger Jordan Graham with an imminent loan move to Fulham this afternoon are believed to be wide of the mark.
Fulham are believed to have enquired about Graham earlier this summer but haven't yet lodged an offer with Wolves.
Wolves could be set for a busy final week of the window. Sources suggest they want to sign a striker and a central midfielder, as well as possibly an experienced left back as cover for Barry Douglas.