The chief executives of Rangers, Celtic and Scottish football's three governing bodies will meet with police and Scottish Government officials, including First Minister Alex Salmond, to discuss the social problems which accompany the fixture.

Scottish Police Federation chairman Les Gray had already called for the fixture to be banned or played behind closed doors before last week's volatile Scottish Cup tie at Parkhead, which saw three Rangers players sent off and coaches Neil Lennon and Ally McCoist clash on the touchline.

More than 30 supporters were arrested at Celtic Park but Strathclyde Police Assistant Chief Constable Campbell Corrigan revealed there had been a 77% increase in processing individuals for violence, anti-social behaviour and drunkenness following the game.

And police confirmed at the weekend they were investigating events during the game following complaints from members of the public.

Topics on the agenda are likely to include the timing of the game, with more midweek matches a possible solution to reducing the anti-social effects of the fixture.

But Gough believes it will always be difficult to contain emotions during the high-pressure game.

Gough said: "It's just my personal opinion, but I think football matters should be dealt with by football people.

"I know there has been a lot of police involvement because seemingly after an Old Firm game domestic violence goes up and stuff like that. That's unacceptable.

"But on the whole I would like to see football deal with football matters.

"Football is an emotional game. I don't think that meetings between politicians will have any difference to what happens in a football game.

"Obviously the managers are now going to warn the players to be on their best behaviour but sometimes games can kick off quite easily."

The resentment between the clubs has arguably intensified since the game with Celtic chief executive Peter Lawwell taking issue with the Scottish Football Association's criticism of his players and Rangers chief executive Martin Bain blaming Celtic's "extreme verbal abuse" of some of their players for the increased tension.

Lennon has apologised for his reaction towards McCoist and declared the pair had moved on from their disagreement, but he was put under 24-hour surveillance after a suspicious package addressed to the Celtic manager, which turned out to be a hoax, was intercepted at an Ayrshire sorting office.

Rangers manager Walter Smith has admitted some of his players lost their discipline at Parkhead but Gough believes the close proximity of the matches increase the risk of that happening.

Celtic's 3-0 win on Wednesday was the fourth Old Firm fixture since the turn of the year and among seven this season, with the next coming at Hampden in the Co-operative Insurance Cup final on March 20.

"When the games are very close together, sometimes resentment carries over," the former Tottenham and Everton player said.

"There was definitely signs of that.

"I have been in situations where we have played Celtic back to back, notably in 1991.

"It was St Patrick's Day, and that was an emotional event at Parkhead, and we ended up losing and getting three players sent off.

"Then we had to go back to Parkhead again and there were huge resentments going over and we lost again, and I think Scott Nisbet got sent off.

"That wasn't a good game for us and I remember having to keep control of myself."

Gough, who was launching the search for this year's additions to the Scottish Football Hall of Fame, added: "Walter Smith came out and said he doesn't like these games and he never has. That says it all.

"As a player, I enjoyed the games on one level. I didn't enjoy the hatred, getting vile abuse shouted at myself at Parkhead, but I enjoyed the challenge. It got me up to play at my best.

"I didn't enjoy the aftermath. The odd times we lost, I wasn't out of the house for a week.

"It's huge pressure on a player and I don't think the public understand the pressure."

Gough can understand how the bad feeling can escalate, pointing to the example of Celtic captain Scott Brown's booking for celebrating his cup equaliser at Ibrox right in front of Rangers player El-Hadji Diouf.

"If you look at things like Brown's celebration, if I was captain I would say 'if we score we have to do the same'," he said.

"It's tit for tat. There has been more animosity and it's been building.

"I could have guessed there would be trouble in last week's game for the team that was losing."

Meanwhile, Celtic have stood by Lennon amid speculation over what was said during his confrontation with McCoist and an earlier flashpoint with Diouf.

The club have taken advice from Paul McBride QC "in light of allegations made regarding Neil Lennon and newspaper reports on this subject".

McBride said: "These allegations are defamatory and outrageous with no substance whatsoever.

"This is a concerted campaign by malicious and despicable individuals to cause distress to Neil Lennon.

"Celtic Football Club and Celtic fans stand by their manager in the face of these vicious and unacceptable attacks."

Meanwhile, Craig Thomson has been chosen to referee the cup final meeting between the teams.

Thomson has taken charge of one Old Firm meeting this season, Celtic's 2-0 Clydesdale Bank Premier League win at Ibrox on January 2, when six players were booked.