“We can do things better but I don’t accept the game is corrupt,” Coates told BBC sports editor Dan Roan.
“The game has never been cleaner and I have been in this game a long time.”
Coates – who first joined the Stoke board in 1985 and, apart from a seven-year absence after fan protests forced him to walk away in 1989, has been at the club ever since – hopes a limit of 10% can be set on transfer commission for agents.
Paul Pogba’s agent Mino Raiola reportedly earned more than £20m from the France midfielder’s £89m summer move to Manchester United through legitimate commission and a clause fixed in the 23-year-old’s deal at previous club Juventus.
While Coates admits a “fear factor” exists that leads to clubs paying high fees to agents to maximise their chances of signing a player in a competitive transfer market, he is hopeful that clubs will mutually agree to restrict payments.
“The amounts are extraordinary, but strangely lots more went on when there was less money in the game,” said the 78-year-old.
“I wondered whether collectively we could agree that we would not pay more than 10% and try and bring some better order into it.
“I think transparency is very important. I would have everything about every transfer deal recorded and the FA and the Premier League or the Football League have a copy.”
The allegations against Allardyce and Wright were both made by The Daily Telegraph on Monday and Wednesday respectively.
Wright was dismissed by Championship club Barnsley on Thursday. A spokesman for the 50-year-old said: “Any suggested acts contrary to criminal law or those of the Football Association and Fifa are categorically denied.”
On Tuesday, the same newspaper claimed eight current or former Premier League managers had taken bribes for player transfers.
The FA, Premier League and EFL have pledged to investigate this week’s allegations.
‘Proud’ Pardew distances himself from England role
Crystal Palace manager Alan Pardew has insisted he would not leave the club if the England role vacated by Allardyce and occupied by Gareth Southgate in a caretaker capacity was offered to him.
“This is where I want to be right now,” he said. “The fans have been terrific with me, it’s a special place for me because I played here. It’s too good to leave.
“Of course I’m privileged and proud to be in that small group that is going to be linked with it – that I’m not going to shy away from.
“The other part is the focus I have to do here and return their loyalty to me, that won’t shake. I won’t let that happen to me.”
‘A black mark on the game’
Everton manager Ronald Koeman said that Allardyce’s departure from his England post was “a black mark on the game”.
The Dutchman, who has previously coached Ajax, Valencia, Benfica and Southampton, added that he has kept himself separate from the financial side of his clubs’ dealings during his managerial career.
“What I know is how I work, and that’s not different in England to when I was in Holland, Portugal or Spain. My advice for a player is technical. I am not involved in the business,” he said.
“If these things are proven right, it needs to be cleaned, to be wiped out of football,” he said.
“I have grown up watching football as a fan on the stands. I am lucky enough to have had a professional career. I have seen the struggles and highs of every single league – the biggest part of that is the honesty and integrity with which we do things.
“We all have that responsibility – mangers, owners, players, fans, agents.”