According to the Los Angeles Times, the newcomer is the favourite to claim the director's chair following reports that Robert Rodriguez has ruled himself out of the running.
Berg is best known for the short film Carousel, and has experience making television advertisements and music videos. He is yet to direct a feature film.
Both 20th Century Fox and Ryan Reynolds - who has been strongly linked with the title role - are said to be admirers of Berg's work.
Reynolds's participation in the project is uncertain due to his involvement in Safe House, R.I.P.D. and the Green Lantern sequel.
Deadpool is scheduled to arrive in theatres in 2012.