The site, which is co-branded with sister concept Buffalo Express, was the burger giant’s first foray in to Europe when it opened in 2015.
The 1,870 sq ft location on Jamestown Road is currently being marketed by Restaurant Property, with an annual rent of £125,000.
Fatburger also opened in London's Wembley in 2017 and Dundee earlier this year.
The chain was founded in Los Angeles in 1947 and began franchising in 1990. It now operates around 200 restaurants in over 20 countries worldwide.
In 2017 the group said it saw “significant opportunity” to expand in the UK and was targeting a further 15 sites.
Numerous US ‘better burger’ brands have crossed the pond in the last decade, but many have struggled to make an impact. Both Steak n Shake (over 500 US sites) and BurgerFi (around 100) have exited the UK less than three years after arriving.
Smashburger opened in Milton Keynes in 2016 boasting a plan to reach 35 restaurants, but so far only seven have opened.
In contrast Five Guys, founded in Virginia in 1986, which launched its 100th UK site this week.