The former Hollywood actor, best known for his role in Terminator, has been asked to return to East London to see how the area has transformed since he lived and trained there as a bodybuilder in the 1960s.
Sir Robin has written to the actor-turned-politician, requesting his presence at his former gym.
Sir Robin wrote: "The reason why I would like you to be in our company is that the vast majority of the Games, some 60 per cent, will be held within Newham - much of it within walking distance of your former training ground in Forest Gate."
The Austrian-born Schwarzenegger was awarded the title of Mr. Universe at age 22 and went on to win the Mr. Olympia contest a total of seven times.
But Schwarzenegger has admitted that much of his success was built on him taking anabolic steroids while they were legal.
He wrote in 1967 that "steroids were helpful to me in maintaining muscle size while on a strict diet in preparation for a contest.
"I did not use them for muscle growth, but rather for muscle maintenance when cutting up."
But that does not appear to have concerned Sir Robin.
He wrote: "You [Schwarzenegger] have been an inspiration to weightlifters and sportspeople since you started winning titles during the 1970s, and have capitalised on your appeal by moving onto acting, and now governing California.
"We hope he'll be back to rekindle the bond."