The so-called Brexit could mean a change to rules governing the signing of players from other EU countries.
"We've maybe got seven or eight players who fall into that category, but how would they do it?" said Canning.
"Would it be done from day one or from renewing a contract? It would definitely affect us in that case."
A BBC report has highlighted that none of the 53 non-British EU players currently in the Scottish Premiership would qualify for a work permit on the basis of their international career alone.
Professor Raymond Boyle, a sports industry expert from the University of Glasgow, has suggested that the rules would be watered down to make it easier for non-EU players to come here - as is the case with Norway and Switzerland.
But Canning, whose club have regularly in recent years complimented their academy graduates with players from abroad, admits it would possibly change their thought process with potential signings.
"One of the first things we do when we look at a player from overseas is ask the question - do they need a work permit?" he told BBC Scotland.
"If that's the case, we generally don't go down that route, so that would definitely have an impact on the club.
"For us to attract an international player that would get the work permit would be difficult, so it would make it a lot more difficult to bring in foreign players.
"Whether that would encourage you to bring through your own, it's something we try and do anyway. I think there's a balance to be struck."
Hamilton Academical may have to change their signing policy if the UK votes to withdraw from the European Union in June, says manager Martin Canning.