Karren Brady, chief executive of Allardyce’s former club West Ham, said she is “both saddened and disappointed” by the developments.
“This is a man who spent his whole life trying to get that job, and got it in his 60s. What a great shame if he loses that job through non-footballing reasons,” she told Radio 1 Newsbeat.
Former FA communications director Julian Eccles has said Allardyce’s actions are “at the very least bad judgement”, and said he will have to justify his claims that third-party ownership is still prevalent.
During the meeting with undercover reporters posing as businessmen, it is alleged Allardyce said it was “not a problem” to bypass the rules and he knew of agents who were “doing it all the time”.
“I think if he is to keep his job at the very least he has to provide the evidence where he says that agents are still involved in this and he has to apologise for stating that these rules are ‘ridiculous’,” Eccles told BBC News.
“We cannot have such a senior figure in our game being so disrespectful of such important rules.”
That view was supported by Match of the Day presenter Gary Lineker, who tweeted saying Allardyce “advising on getting around third-party rules” was the “biggest problem”.
Third-party ownership of players was banned by the FA in 2008.
It is further alleged by the paper that a deal was struck with the England boss worth £400,000 for him to represent the company to Far East investors and to be a keynote speaker at events.
However, Allardyce told the undercover reporters that any arrangement would have to be cleared by the FA.
Allardyce is set to name his second England squad on Sunday, before the World Cup qualifier against Malta on 8 October.