Members of the John Muir Birthplace Trust are to launch an action plan to tempt the star to visit the East Lothian town.
Schwarzenegger, the governor of California, is an admirer of Dunbar-born conservationist Muir, and chose an image of him as the face of California's 25 cent coin three years ago.
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Hide AdThe star visits Britain at the end of September to address the Conservative Party conference in Blackpool, and the trust hopes to lure him north during his stay.
Trust treasurer Will Collin said: "It would attract huge media attention and help raise the profile of John Muir's birthplace."