"A number" of football clubs have allegedly used gagging orders to silence players speaking out about abuse, it is claimed.
Edward Smethurst, a lawyer representing victims, said "calls and emails are coming in all the time" from players saying they were forced to sign non-disclosure agreements in return for compensation.
It comes after Chelsea FC apologised to former player Gary Johnson for the abuse he suffered as a trainee in the 1970s.
He was asked to sign a £50,000 confidentiality clause after he made allegations of abuse.
Speaking at the launch of The Offside Trust, an independent organisation set up by former footballers who suffered abuse, Mr Smethurst said: "It's unfolding as we speak. It's a number. It's several (but) less than five."
The trust has also received allegations against people who still work in the "senior echelons" of the sport, he said.
The trust was set up by former Crewe Alexandra players Andy Woodward and Steve Walters and Chris Unsworth, an ex-Manchester City youth player.
Woodward, whose interview with The Guardian nearly three weeks ago started a wave of allegations, said he and his partners are "fighting for justice" and trying to support fellow victims.
Mr Smethurst said fresh claims of historical sexual abuse at clubs are being made "all of the time".
"There are certain names who are coming in who do come up repeatedly," he added.
The award-winning lawyer, who also chairs the Madeleine McCann Fund, said it was important that clubs "should not hush these things up and tie victims up in confidentiality".
"We think there's a wider perspective here and that's the protection of victims and preventing these things from reoccurring. It's often the case that when these things go public, other victims come forward."
According to police, new lines of inquiry are being followed at 55 clubs around the country.
Last week, the FA asked Kate Gallafent QC to lead a review of its response to historical allegations of sexual abuse.
While Crewe have launched an independent investigation into alleged wrongdoing in their youth set-up.
- Contact The Offside Trust here