The Star Trek filmmaker, who directed the third movie in the franchise, recently confirmed that he will produce the sequel along with series star Tom Cruise.
Abrams told Sci-Fi Wire that he received a phone call from Graves's representative who said that the actor is interested in taking part in the follow-up. The 83-year-old portrayed Jim Phelps, the head of an elite group of agents, on the original series from 1967 to 1973 and reprised the role for a short-lived late '80s TV show.
"I just got a call that Peter Graves is in great shape, which would be a very bizarre bend in the space-time continuum, for obvious reasons," Abrams said.
The Lost creator also stated that he is open to feature original Mission: Impossible actors in the cinematic version. Trek's resident Vulcan Leonard Nimoy played Paris for 49 episodes on the TV programme, before starring in Abrams's recent blockbuster reboot.
He added: "Whether it's Nimoy, who I have an incredible affinity for, or Graves, or anyone, we'll see."