Criss would do a three-week stint preceded by two weeks of rehearsals on the musical, which was revived this past March and recently won a Tony award. If the deal goes through, he would have to miss an episode-and-a-half of Glee. However, series co-creator Ryan Murphy reportedly encouraged Criss to take the chance, according to Deadline.
Criss, who made his Glee debut last November, was recently promoted to series regular along with Harry Shum, Jr. He toured with the rest of the Glee cast around the United States, England and Ireland and will appear in Glee: The 3D Concert Movie.
After Criss' proposed run, How to Succeed in Business Without Really Trying is still looking for Radcliffe's permanent replacement, as well as an actor to take over John Larroquette's role.
Season 3 of Glee premieres on Tuesday, Sept. 20 at 8/7c on Fox.