The American burger restaurant, which took over from Baroosh which closed at the end of January, has applied for its premises licence to Hillingdon Council.
If approved, it will open from 11am to 12 midnight on Fridays and Saturdays and 11am to 11pm every other day.
A Five Guys spokesman said the Uxbridge branch is scheduled to open in early June and construction was set to begin at the end of March.
The family chain has more than 1,000 restaurants in America across 47 states. Its first UK branch opened in Covent Garden in July last year and since then three more have opened across the south of England.
President Obama bought lunch for him and his colleagues at the Washington Five Guys branch in 2011. Next time he is in the UK maybe he will come to Uxbridge.
The site in Uxbridge town centre is currently encased with Five Guys-branded boards.