NBC bosses are reportedly hoping that the actor will make an appearance on the show on Saturday (October 8), when it will be hosted his Tower Heist co-star Ben Stiller, according to the New York Post.
Murphy was a regular cast member of Saturday Night Live from 1980 to 1984, until his public feud with creator Lorne Michaels.
The comedian was recently confirmed as host of next year's Oscars, which will be produced by Tower Heist director Brett Ratner.
Murphy also recently revealed that he is "tempted" to make a return to stand-up comedy.
Saturday Night Live will air on NBC on October 8 at 11.30pm/10.30c.
Watch clips of Eddie Murphy's time on Saturday Night Live below: