Emirates' President Tim Clark also warned Boeing rival Airbus not to let the A350 jet program run up three years of development delays, similar to those seen on Boeing's 787 Dreamliner.
"The 777 and its derivative is of great interest to us because we started taking the 777-300ERs in 2005 and they will start retiring in a 12 year period," Clark said in an interview with Reuters Television on Thursday.
Boeing is considering a refresh of its 777 with new wings and new engines to enter service near the end of the decade.
Clark said Boeing was "nearly there" in terms of what Emirates expected from the revamped 777.
"We've been working with them for quite a long time and are a little bit exasperated by the time its taking. My view is that a significant number of carriers will sign up for this airplane."
He said Boeing was having difficulties in trying to work out the recurring costs.
"I believe the demand is there. Anybody who has a 777 today of size of ER will be automatically interested in its derivative."
Clark gave a lukewarm response to Airbus's decision last year to beef up the largest A350-1000 variant with bigger engines and more range, while pushing its development back two years.
"Well, I'm just saying we are watching it very closely. We don't want to get caught in the same way as the 787s ... we can't afford a three year delay on this," said Clark.
"We went to the A350 because they sized it to the level we needed it to be."
Emirates has 20 A350-1000s on order.
Airbus pushed back development of the stretched A350-1000 by two years when it decided to overhaul the design last year. The $320 million jet is now due to enter service in mid-2017.
The European planemaker suffered a fresh setback last week when Abu Dhabi-based Etihad Airways halved its order for the A350-1000 over four months, dropping to 12 in April from 25 in November.
Airbus has not sold any of the largest variant of its next-generation A350 since updating the design with bigger Rolls-Royce engines last June, while Boeing has been notching up record orders of the wide-body 777.
Airbus says it is confident a market will flourish for the long-distance jet and has said its only difficulty is the shortage of available delivery slots before 2018 or 2019.
"It's up to them (Airbus) to deliver the airplane to the specification that we have contracted ... and that's what we continue to watch," said Clark.
