The FA chief executive was speaking at a news conference on the day it was revealed that a new, dedicated NSPCC helpline for football received 860 calls in its first week and 15 police forces around the country have confirmed they are investigating fresh allegations of historic abuse.
When asked about reports that some clubs may have paid off alleged victims in return for their silence on the matter, Glenn said this would be investigated by both the police and the FA's independent review.
Sitting alongside newly-appointed England manager Gareth Southgate, Glenn said: " We've committed to a full review, shining the light on what happened in the past in football
"We have clear rules in the game and if there's any evidence of a breach of those - and hushing up would be one - subject to due process, the police need to be at the right place in this, when it's our turn to apply the rules we absolutely will, regardless of size of club."
When pressed on the possible existence of non-disclosure agreements and gagging orders, Glenn said: "I can't say if there has been a cover-up in the game (but) I doubt it."
Glenn's comments come a day after the Daily Telegraph reported an allegation that Chelsea made a confidential payment to a former youth team player who accused the club's ex-chief scout, Eddie Heath, of sexually abusing him.
The player is reported to have made the allegation, which relates to possible offences in the 1970s, in the last three years
Heath died before the allegation was made.
On Tuesday, the club issued a statement to say it has "retained" an external law firm to carry out an investigation into an individual employed by the club in the 1970s, who is now dead
It added that it would fully co-operate with the FA's wider investigation but would make no further comment while those inquiries were ongoing.
Earlier that day, FA chairman Greg Clarke outlined the scope of the governing body's investigation, which is being led by Kate Gallafent QC, and told reporters that he found the idea that any victim had been paid off to protect a club's image as "morally repugnant"
FA head of equality and safeguarding Sue Ravenlaw added that it could also be illegal.
This point was picked up by Glenn today.
The former Leicester director said: "If there are restrictive contracts, through employment law, which prevent people from speaking out about a crime, because that's what we're talking about, then it must be dealt with.
"But the primacy needs to be sorted out: where does the police get involved, where does the FA? But the only way this gets dealt with is through openness and honesty."
Source : PA
Source: PA