From Aviation Week & Space Technology:
Only the 63,300 lb. thrust General Electric CF6-80C2B9F is a committed engine for the 747XQLR thus far. It is a variant of the 62,100 lb.-thrust -80C2B5F that GE offers for the 747-400 and 747-400ER.
Boeing is in talks with Pratt & Whitney and Rolls-Royce as well, and both are expected to join the program if it is launched. Pratt will offer an adaptation of the 63,300-lb.-thrust PW4062 that it has on the -400/-400ER. Rolls would switch from the RB211-524H8-T on the 747-400ER to the Trent 600, a company official said.
Having all three engines available will be a key to the -400XQLR's acceptance, particularly in Asia, where the new version is targeted. For instance, SIA and Korean Air are Pratt & whitney customers for thier 747 fleets, while Cathay Pacific flies Trents on its 777 fleet and All Nippon Airways and Japan Airlines fly the CF6-80C.
It appears that Boeing has learned a lesson from the 777LR.