Peter Lawwell last night pledged to take action if the "Big Jock Knew" campaign persists in grounds around the country.
The Celtic chief executive conveyed his outrage at the slogan, chanted by rival fans in reference to the child sex abuse charges for which the former Celtic Boys' Club manager, James Torbett, was found guilty.
The campaign has grown in popularity since attempts were made to nominate Jock Stein for a posthumous knighthood.
It is also regarded as a loophole' for Rangers fans who have been sanctioned for signing the outlawed sectarian song The Billy Boys. Chants, banners and stickers have also been evident at other grounds, with Hearts fans heard chanting the slogan during a recent league match at Parkhead.
Gordon Smith, the Scottish FA chief executive, also insisted in having a banner carrying the words removed during a Scottish Cup tie between Newton Stewart and Linlithgow Rose.
Last night, Lawwell explained Celtic's silent stance but, with the blessing of the Stein family, warned the club would act if the campaign does not abate.
"It is a poisonous, repugnant, despicable and even cowardly campaign,"
he said. "He is one of Celtic's greats, Scottish football's in fact, and this campaign is nothing short of disgraceful.
"In the context of this week in Scotland, when we came close to qualifying for the European Championships, it should be remembered that this man died managing Scotland, taking them to the World Cup finals.
"We haven't responded because we didn't want to dignify it with public statement, but we have been working behind the scenes and have spoken with the family, who are content with the way we are dealing with it.
"If the problem escalates, we will have no option but to do something else. It is totally disrespectful to one of Celtic's favourite sons and we are not taking it lightly."
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