New Hoops boss Ronny Deila started putting his squad through their paces on Tuesday and will take them to Austria for a fortnight as preparations continue for the new campaign.
While the Norwegian is unlikely to make sweeping changes to a squad which claimed Celtic's third straight Premiership crown, there are several players on the periphery of the first team that need to catch the eye this summer. And former boss Hay knows the fringe Bhoys will have to up their game to convince Deila they are worthy of a green and white jersey next term.
He told SportTimes: "All the players will be trying to impress him, but there are some more than others who have to do that bit
extra after not featuring much last term.
"The team almost picks itself from last season,
though there are one or two areas up for debate.
"What might happen is that guys who didn't get a chance, taking the likes of Teemu Pukki as an
example, will see this as their opportunity to
impress the new manager.
"He will hope that will lead to more chances in the starting line-up. If you had to pick a team now, he probably wouldn't be in it.
"He and others might have impressed under Neil Lennon if he had stayed, the new season could have been a fresh start.
"There are a few others in a similar position. They need to impress and get more game time than they did last season."
Deila confirmed he is unlikely to delve into the transfer market before Celtic kick off their Champions League campaign against KR Reykjavik in Iceland on Tuesday, July 15, with the return leg at Murrayfield a week later.
The Hoops are bidding for a third group stage appearance in three years and will use their fortnight in Austria and handful of friendly fixtures to ensure they are able to hit the ground running.
And Hay reckons the change in the Parkhead dugout could be the vital spark some of the misfiring Hoops stars need this summer. He said: "Players may feel they weren't given a chance or it can take time for them to settle in and you don't see the best of them in the first season.
"Even without a new manager coming in, players see the new season as a fresh start. It is another chance to kick-start their Celtic careers."