Glenn was speaking about Manchester City manager Pep Guardiola wearing a yellow ribbon in support of Catalan independence. The former Barcelona coach is facing FA charges for breaching rules forbidding the display of political symbols.
Glenn said he wanted to keep such symbols out of the game and that the British tradition of wearing a poppy to remember the country's war dead was not a political matter.
"Things like a poppy are OK but things that are going to be highly divisive are not. And that could be strong religious symbols, it could be the Star of David, it could be the hammer and sickle, it could be a swastika, anything like Robert Mugabe on your shirt, these are the things we don’t want,” Glenn said.
"And to be honest and to be very clear, Pep Guardiola’s yellow ribbon is a political stance, it’s a symbol of Catalan independence," he added.
"Where do you draw the line? Should we have someone with a UKIP badge, someone with an ISIS badge?”
Glenn's comments were criticised by Jewish Leadership Council CEO Simon Johnson who said the examples used were "ill-judged and in poor taste".
"The Star of David is a Jewish religious symbol of immense importance to Jews worldwide. To put it in the same bracket as the swastika and Robert Mugabe is offensive and inappropriate," Johnson added.
"We will raise formally with the FA the Jewish community's deep disappointment with this statement."
Glenn said he would be speaking to the Jewish Leadership Council and anti-racism group Kick It Out to apologise personally.
"I would like to apologise for any offence caused by the examples I gave when referring to political and religious symbols in football, specifically in reference to the Star of David, which is a hugely important symbol to Jewish people all over the world," Glenn said.
Spaniard Guardiola has until Monday to respond to the ruling body’s charge that he displayed a political message.
(Reporting by Simon Evans, editing by Ed Osmond)
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