But the former Parkhead manager isn't in favour of re-allocating trophies to the runners-up in the various com-petitions the Ibrox club secured during the period back to 1999.
Hay said: "I believe, if it is proven Rangers are guilty of breaching SPL rules, then the titles would have to be stripped. You have to remember this is a completely separate matter from punishing the club for entering administration or liquidation. This is about allegedly operating dual contracts during a lengthy period of time in which the use of them offered an unfair advantage over other teams."
The SPL's investigation into the use of alleged dual contracts is on-going, although evidence is believed to have been found that Rangers have a case to answer which could cost them the seven titles won within the period in question.
It could also turn out to be the case that the SFA would then be forced to look into doing the same in the cup competitions Rangers have won.
In Italy, Juventus were stripped of title successes by the Italian FA in light of a match-fixing scandal and Hay said: "If all the facts are on the table, and the SPL and SFA find Rangers guilty, then I do think there is every likelihood the respective punish-ment could be to strip them of titles or other trophies won during this period.
"What I wouldn't be in favour of is then awarding the titles or anything to whatever team finished second in the league, or lost a cup final. That wouldn't be right either.
"Yes, some people might argue they might have won them had the alleged dual contracts not been in place, but that would be dealing with ifs and buts.
"The SPL and the SFA can only deal with the facts in front of them. It will all become clear in the coming weeks. The history books will either be altered or they won't.
"I'm sure there will be a number of Rangers fans who will still argue the point that their club won the competitions and you can't change it now.
"However, if they are stripped of the titles then it will be down in black and white."