New boss Ronny Deila will find out who his side will face in the second qualifying round for Europe's premier competition when the draw is made in Nyon on Monday.
The Scottish champions will have to chart their way through two qualifiers and a play-off to reach the group stages for a third consecutive season.
And Hay reckons the Parkhead board will wait to see if the big Euro money is banked before giving Deila the chequebook to bolster his squad this summer.
He told SportTimes: "You might get the odd player that will come in before a place in the Champions League is secured, but I think Celtic will wait to see what the outcome is in the qualifying stages.
"Players will do the same. You will find that the lure of playing in the group stages compensates for the fact they are playing in Scotland.
"It is a two-way thing. The club can get caught in a dilemma but a player will more often that not wait to see where Celtic are playing before committing himself.
"The manager will be looking at players, but he doesn't need to change too much early doors, I think the squad is good enough to get to the group stages.
"There will be fresh additions, but they might not come before the qualifiers."
While Deila and new assistant manager John Collins will spend the coming days and weeks looking for ways to improve their squad, their biggest challenge could be holding on to some of the Hoops'
current prize assets.
Defender Virgil van Dijk has been linked with a move to Southampton in recent days and Hay hopes the lure of more European action will persuade the stars to stay at the club.
He said: "There is speculation about Van Dijk, there will be more talk about Fraser Forster and maybe some other players, but everyone knows how important it is to hold on to these types of players.
"I think the likelihood is that Van Dijk will stay, there is maybe more of a chance of Forster leaving after the World Cup.
"Celtic are well aware of the importance of keeping both of them and Peter Lawwell has said they don't need to sell.
"They might be able to hold on to them until they qualify for the Champions League, if they do, and the decisions could be taken after that.
"If they qualify, they might want to stay put. They could go down south and earn more money but not necessarily play in the Champions League.
"That might have an influence on whether they stay or not."