Kitchin posted on social media site Instagram that the former Manchester United midfielder had been to his restaurant The Kitchin, on Commercial Street in Leith for lunch today (Thursday).
Writing on Intsagram, Kitchin said: "This is how we roll on Thursday lunch in Leith.. @thekitchin
"Thanks for taking the time to say hello to all the team (very classy)."
Beckham, 44, was snapped at Finnieston's Crabshakk seafood restaurant in Glasgow yesterday.
The former Manchester United, LA Galaxy and Real Madrid midfielder is understood to be in Scotland in his capacity as ambassador for the Haig Club whisky brand.