Gene Hackman shockingly does not have a star on the Hollywood Walk of Fame for fans to grieve their loss … but there is a restaurant in New Mexico where some are paying their respects to the legend.

Doug Lanham, a close friend and former business partner, tells TMZ … fans have begun dropping off notes and flowers to his Santa Fe restaurant Jinja Bar & Bistro … which was co-owned by Hackman for several years after he walked away from Hollywood a two-time Oscar winner and film icon.

In addition to being regarded as one of the best actors to ever grace the silver screen … Hackman was also a prolific painter — and did nearly all the amazing work that hangs from Jinja’s walls.

As we previously reported … despite leaving the restaurant industry, Doug says Gene would often come by for a meal — and usually pick up the tab for customers.

Doug remembers Gene as a jokester who would play silly little tricks on him … like putting his finger to Doug’s back and telling him to “reach for the stars” — pretty hilarious given Gene won an Oscar for the western flick, “Unforgiven.”

Gene and his wife Betsy were found dead in their home Wednesday — and an investigation into just what happened is ongoing. Santa Fe authorities said on Friday Gene’s pacemaker showed its last event was on February 17 … making investigators believe that’s when he died.

Gene was 95 … Betsy was 65.