Detroit Pistons guard Gordon has expressed his desire to play for the country of his birth for a number of years but has yet to make his debut while Charlotte Bobcats centre Mullens, whose mother was born in London, only received his passport last month.
Deng, the first British player to appear in an All-Star game earlier this year, has long been a talisman of the side but knows he can't do it alone and has admitted delight about the new additions.
Finch names the US-based stars in a squad of 21 that will be trimmed in the coming months, with just 12 announced on the final Olympic roster in early July.
“I am very excited to pull on the GB jersey this summer and play for my country. To be invited into camp is the first step in that journey and I am immensely proud to have the opportunity," said Gordon.
“I am totally committed to playing with the Standard Life GB team this year and look forward to being part of the squad hoping to make 2012 a year to remember for British Basketball fans.”
Meanwhile, former NBA player Pops Mensah Bonsu returns to the national team after missing last year's EuroBasket through injury.
He has been impressive with Turkish club side Besiktas in recent weeks, while established national team regulars Joel Freeland and Robert Archibald have enjoyed strong seasons in the high-quality Spanish top flight.
But just two of the squad, Sheffield's Nate Reinking and Leicester's Andrew Sullivan, ply their trade in the British Basketball League - underlining recent comments by John Amaechi about the strength of the domestic game.
"The GB basketball programme has come a long way since 2006 and the blend we have now of experienced talent with the younger guys is fantastic to see," said Finch, whose side will play a series of warm-up games, including a clash against the USA, in the build-up to their first Olympic campaign since 1948.
"We have the potential for a world class team who will surprise a few people this summer.
"The commitment from all our players to the programme once again is great and it’s also good to see our strength and depth continuing to increase year on year.”