Chicago Bull's forward Deng has been a key player for Great Britain in recent years while Charlotte Bobcats centre Mullens, whose mother was born in London, only received his passport in March.
Detroit Pistons guard Gordon has yet to make his Team GB debut and is delighted to have been included in the set-up.
"I am very excited to pull on the GB jersey this summer and play for my country," Gordon said.
"To be invited into camp is the first step in that journey and I am immensely proud to have the opportunity."
Coach Finch has named his 21-man squad that will be trimmed in the coming months to just just 12 players in early July.