The soccer superstar - who moved to America three years ago when he signed a deal to play for the Los Angeles Galaxy team - is reportedly planning to run the pub with TV chef Gordon Ramsay and name it after his former Spice Girl wife Victoria.
Close pals David, 35, and Gordon, 43, have been talking about running a business together for years, and now believe a traditional English drinking establishment would be successful with locals.
There are a string of expats who live in Los Angeles who would be keen for somewhere to go with traditional ales and beer on tap as well as an English food menu.
A friend of David's told the Daily Star newspaper: "He wants pie and mash, fish and chips and even chicken in a basket on the menu, just like the meals he eats when he's in the UK."
The friends have previously spoken publicly about setting up a restaurant together, and it is something their wives Victoria, 36, and Tana, 36, are said to be support.
After Gordon and Tana - along with their four children - went to the Beckhams' house last Christmas Day (25.12.09), the fiery chef revealed the two families worked well together in the kitchen.
He said: "We had a great time together, a lot of fun and a lot of laughs - just cooking and having fun.
"So maybe one day we will have a restaurant together! Who knows?"
After moving to America to play for Los Angeles Galaxy, David - who has three sons with Victoria - admitted one of the things he missed the most about Britain was a "lager shandy" and a roast dinner in a pub on a Sunday.
He said: "I miss English pubs - having a good lager shandy and a Sunday lunch while watching the football."
Speaking about the possible pub venture, a spokesman for David said: "There are no plans in the pipeline, but never say never."
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