"Jamie is delighted that the film is breaking box office records worldwide and whilst the studio has not made any formal announcements about sequels, he is looking forward to making the next film," his rep told ABC News.
The film has made more than $400 million worldwide thus far since being released just two weeks ago, according to USA Today.
In the hit BDSM movie, Dornan, 32, stars as Christian Grey, the man whose interests "are very singular in nature" and include on-screen bondage with co-star Dakota Johnson. Dornan married Amelia Warner in 2013 and the two welcomed their first child last year.
Since the rumors, Universal Pictures had no official comment on the report, adds USA Today.
Dornan took over the lead for the blockbuster movie after "Sons of Anarchy" star Charlie Hunnam backed out of the movie in 2013.