The discussion began after President Donald Trump's star on the Walk of Fame was vandalized, prompting the Hollywood City Council to vote to remove the star permanently.
That's when Hamill came up with the idea to replace Trump's star with one for his Star Wars co-star Carrie Fisher, who died in 2016.
"How about replacing [Trump's star] with someone who really earned it? Like Carrie Fisher," Hamill tweeted.
Many fans were surprised to find out that Fisher didn't already have a star, having assumed the beloved actress was already recognized on the Walk of Fame. Shatner, it turns out, was one of those surprised fans.
"Hey Star Wars is it true that Carrie Fisher does not have a star on the walk of fame?," Shatner tweeted on Monday, about a week after Hamill first suggested the idea. "If it is what are we going to do about it?"
Shatner went on to tweet that he had reached out to Fisher's family before pursuing the matter any further.
"I just asked a member of Carrie's family if there are any issues," Shatner tweeted. "Again let's see what they say first before we do anything."
The Walk of Fame, according to its website, only allows for the addition of one posthumous star per year. There is also a five-year waiting period before a star can qualify for a posthumous star. That means that, based on those rules, Fisher will not be eligible for her star until 2021.
Shatner adding his voice to the call for Fisher's Walk of Fame star follows his revealing that Fisher once asked him to sign a Slave Leia photo.
Fisher died at the age of 60. She returned to her role as Leia Organa in 2015's Star Wars: The Force Awakens. She appeared again in Star Wars: The Last Jedi, which was released a year after her death. Lucasfilm has confirmed that she will appear as Leia once more using previously shot footage in Star Wars: Episode IX in 2019. That film will complete Star Wars' sequel trilogy and the Skywalker that began in the original Star Wars in 1977.
Do you think Carrie Fisher should be added to the Hollywood Walk of Fame? Let us know what you think about it in the comments!