Triesman, who has brokered a deal with FIFA for Britain to enter a team at the 2012 London Games, said it would be desirable to have an Englishman in charge.
He hinted Fulham manager Roy Hodgson and England under-21 coach Stuart Pearce could be in contention.
However, Triesman ruled out Scots Alex Ferguson (Manchester United) and David Moyes (Everton) as that would break the FA's deal with the other home nations about choosing an all-English side.
"I would be very disappointed if we have not appointed a coach for the Olympic team by the end of this calendar year," Triesman told Reuters in an interview.
"The age of the coach is not as important as his ability to get the best out of young players, some of whom might still only be 17, 18 or 19 now but 20 or so when the Olympics come around.
"I think the coach needs that length of time to identify the players who will make up his squad and start working with them to develop a team spirit," added Triesman.
"We cannot appoint a Scot, Welshman or Northern Irishman because that would go against our agreement with the other home nations. It would be very desirable to have an English coach."
The FA chairman, though, did not rule out the prospect of employing an overseas coach.
"Having a foreign coach is not entirely out of the question but it will be fantastic to have an Olympics on home soil so it would be great to have a home-grown coach if we can," said Triesman.
WORLD CUP
"The most important thing is who would be the best person and we also have to ensure any appointment does not interfere with the preparations for the 2010 World Cup."
Triesman spoke in glowing terms of Pearce's spell with the under-21s.
"I'm not going to speculate about names but I'm a great admirer of Stuart Pearce and I think his work with the under-21s has been superb," he said.
"He got an English team through to a final (this year's Euro under-21 championship) for the first time for quite some time. He could be someone who fits the profile."
Britain, who won the Olympic football title in 1908 and 1912, last competed in the competition proper in Rome in 1960 and last took part in the qualifiers for the 1972 Munich Olympics when they were eliminated by Bulgaria.
They have not entered a team in the Olympics since then because there is no British national side affiliated to world football's ruling body FIFA, with England, Scotland, Wales and Northern Ireland affiliated as separate countries.
Although president Sepp Blatter has given Scotland, Wales and Northern Ireland assurances their autonomy is safe within FIFA, and guaranteed since 1947 by FIFA statutes, they have declined to participate in the 2012 Games as they do not want to endanger their positions.
"That is a regret but I respect their positions," said Triesman. "The decision has now been made and accepted by FIFA that we will have an English-only team.
"You never know it
