Former England rugby union international
Moore, 50, who played in the 1991 Rugby Union World Cup final, nevertheless believes such a step could help to clean up football's image.
Following Chelsea's allegation that referee
Press Association Sport understands 37-year-old Clattenburg completely denies the allegations against him, which are the subject of investigations by the
The Ref! Link system has been successfully deployed in rugby, allowing fans an insight to discussions between players and officials during matches.
Moore said: "Not only do you record these things but you put them on the Ref! Link so that the crowd including the children and the sponsors, most importantly, can hear what they say."
Moore, a Chelsea supporter, said football's language would be toned down "within six weeks" of such a scheme.
"But when you speak to people in football, a lot of them say 'You can't do that'," Moore told BBC Radio Five Live.
"But I say, 'You can do it, you just won't'. And 'can't' and 'won't' are very different things."
He added: "There's no technical reason or moral reason, it's just that they're afraid people will actually hear just how bad it is.
"If you want to change something, then you will do something. The solution is available."
Moore understands why referees do not typically exercise their right to book players for swearing or other bad language.
"They would never be supported by the Premier League or the FA and they would be the ones who would never ref again," Moore said.
"While they have the power to deal with it that way, I understand why they don't."
English Premier League
Aston Villa boss Paul Lambert has warned Christian Benteke he faces a "reality check" after reports suggesting the striker could be keen to leave the club.