Haaland has made a stunning start to the season for BVB, scoring 11 times in eight appearances, and he has now netted 68 goals in 67 outings for the German giants in all competitions.
A £67m release clause in the 21-year-old's contract will become active next summer, and a number of clubs are expected to battle for the Norway international's signature.
Rice, meanwhile, was strongly linked with the Red Devils over the summer but remained at the London Stadium, with the Hammers thought to value him at £100m.
Luckhurst said that "a season of capacity crowds, revenue up and staggered spending this summer would make it affordable to sign both next year" when asked about the pair during a Q&A.
Rice, who excelled for England at Euro 2020, still has three years left to run on his current deal at West Ham but is believed to be keen to secure a move to a Champions League club next summer. body check tags ::