Speaking at the Soccerex global convention on Wednesday, Glenn was asked about the alleged reputation the FA has for arrogance within the international game.
“I think we are perceived as arrogant. I don’t think we necessarily are but perceptions… it does matter,” said Glenn, who took up his position in March.
“As a relative newcomer coming in, the ultimate expression of arrogance, and we don’t even see it, but we refer to ourselves, we go to international conventions and say, ‘Hi, I’m Martin Glenn and I am from the FA.
“Which one? Obviously the English, because we invented it. Every other is the German association, the French association, we are so assumptive,” he said.
Asked whether a change of name would be a solution, Glenn said: “Possibly, it is not an ultimate priority.
“But what is seen to be the case is that we get interested in the international game when it suits our purposes. We’re seen to be — you want to host a World Cup, suddenly you got very friendly.
“So, it is a global game, we have to build global alliances and be seen to be a force for good,” he added.
England lost out on their most recent bid to host the World Cup with Russia earning hosting rights to the 2018 tournament.
The only time England staged the tournament was in 1966, when they won their only world crown.
Glenn said the FA was respected for its ability to promote football and for the fact the game is run in a clean fashion but that more time was required to build relationships globally.
“We just need to make sure that we spend enough time when we go to international meetings to talk to them, share ideas.” he said.
“It matters because when it comes down to a 50-50 decision on whether we get a tournament or not we would like to get the benefit of doubt.
“The fact that we have got the semis and final of Euro 2020, is a good sign of the re-engagement that happened before my time, where people see us as part of the team as opposed to selectively choosing to be part of it when it suits us.”
(Reporting by Simon Evans; Editing by Ken Ferris)