City manager Malky Mackay has been an admirer of the 23-year-old for some time and believes Moore, who joined the Bees in 2009, has a big future.
"It'll be paperwork first thing Monday morning, that's the only thing holding that one up," Mackay told the Hounslow Chronicle.
"I'm glad to get that one in, he's someone we've tracked for a year and he's had a successful year for Brentford.
"He's one that I think is a real prospect. For the future of the club, I've got three really good goalkeepers now; Simon comes in and I think he can kick on again.
"My thanks to Brentford for the way they went about their business, they were very professional and it was done very quickly."