The actor, who is one of the stars of 30 Rock, is seeking to gain ownership of the domain TracyMorgan.com and has brought his case to the World Intellectual Property Organization Arbitration and Mediation Center.
Although the web address has been active since 2004, Morgan is now keen to take control of not only the URL, but also the content it is displaying.
As a US-based artist, owning the simplest .com domain available would be an excellent way for Morgan to improve his online presence.
The move, if successful, will also prevent people from being to use the name in bad faith, by either redirecting them to other websites, or trying to sell counterfeit goods.
UDRPs seek to resolve trademark-based domain name disputes through agreement, court action or arbitration.