Portrush - which last hosted the Open in 1951 - was awarded the honour in October 2015 before the 2016 referendum in which Britons voted to leave the European Union.
The uncertainty surrounding Brexit - and in particular the backstop to retain an open border on the island of Ireland - is causing headaches for golf's governing body ahead of the tournament which runs from July 18-21.
"Like every business, and I think about the Open as such, the lack of certainty about the rules, the law in which we are operating under post-March 29th has caused us significant concern," Slumbers told a press conference on Tuesday.
"In hindsight, would I be wanting to do Portrush in the year that we would be potentially leaving the European Union without a deal? No.
"We, as a management team, have spent a lot of time looking at contingencies and what we need to do.
"The future of the border is the number one concern.
"We have over 2 000 containers to get across the Irish Sea and we start building on April 2."
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Slumbers, who said the tournament is a sell out with 70 percent of the spectators from Ireland, said that contact with ministers had not resolved the logistical conundrum of which port to use to bring in the containers, some from as far afield as the Middle East.
"We have engagement with ministers and Parliament but the concern is all around certainty," he said.
"If you know the rules you're playing by then you can play, you optimise what you've got.
"The problem is we don't know whether to reschedule to bring all our containers in through Dublin, whether to move them through Belfast, whether to ship them out of the UK now."
Slumbers, though, said the spectators will not notice and the show will go on regardless.
"It doesn't threaten the staging, we will make it happen," said Slumbers.
"It's just more complex than we anticipated.
"For the insiders it's a bit harder but for everyone outside it won't impact at all, they won't notice."
Brexit is not the only headache for Slumbers. Portrush management have had to build two new holes because the tented village for the tournament has supplanted the two closing holes.
"Someone said to me when I was out for the Latin American amateur championship 'You must be looking forward to Portrush' and I said well actually I'll be quite pleased when it's over," said Slumbers.