Chelsea have apologised to former player Gary Johnson, who was abused by late chief scout Eddie Heath, after waiving a confidentiality clause in a 50,000 pounds ($63,850, 59,230 euros) agreement they made with him.
Lawyer Edward Smethurst, who helped set up the Offside Trust for abuse victims, said players forced to sign non-disclosure agreements in return for compensation were coming forward "all the time".
"Certainly, the allegations have been made by victims that confidentiality clauses have been used in relation to other clubs, but I'm not in a position to independently verify this," he was quoted as saying by British newspapers on Tuesday.
"It's unfolding as we speak. It's a number. It's several, (but) less than five."
The Offside Trust, set up by abuse victims Andy Woodward, Steve Walters and Chris Unsworth, launched in Manchester on Monday.
Since Woodward came forward three weeks ago to reveal he was abused by convicted paedophile Barry Bennell during his time at Crewe Alexandra, a wave of allegations has swept through British football.
Eighteen British police forces are investigating claims of sexual abuse spanning four decades and lines of inquiry are reportedly being pursued at 55 clubs.
Queens Park Rangers are the latest club to have been touched by the scandal, the London side revealing they have been made aware of allegations against former chief scout Chris Gieler, who died in 2004.
"The club takes these allegations very seriously and will cooperate fully in any forthcoming investigation," the second-tier club said in a statement.
"Any form of abuse has no place in football or society."
Smethurst, who is based in Manchester, said the same names were being repeated by abuse victims and some alleged abusers were still working at the highest levels of the sport.
"There are specific allegations against specific individuals, many of whom have been rumoured to be involved for a long time, some of whom still work in the senior echelons of football, and it's extremely worrying," he said.
"There are certain names who are coming in who do come up repeatedly."
England's Football Association announced on Tuesday that a new lawyer has been placed in charge of its internal review of the scandal.
Barrister Clive Sheldon has replaced Kate Gallafent "in the light of the increased scope of the review" and "with respect to her other professional commitments".
Sheldon's previous work includes a number of investigatory reviews involving matters of child protection and safeguarding.
The FA also revealed the terms of reference for its review, which will "commence immediately" but has no fixed deadline.
"The precise number of players, alleged abusers and clubs as yet is unknown," the FA said in a statement.
"The FA has determined that it is necessary to instruct external leading counsel to conduct a review into what if anything the FA and clubs knew about these allegations at the relevant time (and) what action was taken or should have taken place.
"The FA continues to work closely with the relevant authorities and respects the ongoing investigation by the police being coordinated by Operation Hydrant into childhood sexual abuse in football."