Ronny Deila's side take a 1-0 lead into the return leg of their Champions League second qualifying round clash - with either St Patrick’s Athletic of Ireland or Legia Warsaw of Poland now awaiting them in the next round. .
With Parkhead unavailable due to the Commonwealth Games, the game will be played at the home of Scottish rugby.
And Celtic legend Hay reckons having a fairly straightforward clash first up should give Celtic an edge when playing the home leg of their third round tie in the coming weeks at the same venue.
He said: "I don't think it would matter where Celtic played the second leg of this tie, they would still beat Reykjavik and get through to the next round.
"The positive of playing at Murrayfield next week is that they will have a chance to get used to it for the home leg of the third qualifying round.
"The opposition in that round will be tougher and it is an advantage to Celtic to have a game under their belt in Edinburgh before that tie."
While Celtic should have few worries on the park at Murrayfield as they look to sail safely through to the next of what they hope will be three qualification clashes, the experience will be somewhat different for the green and white faithful.
The Hoops are unlikely to get anywhere near filling the 67,000 capacity stadium and recreating the famous Parkhead Euro night atmosphere.
But former boss Hay hopes as many fans as possible head for the Capital as they get their first glimpse of Ronny Deila's side in action on Scottish soil this season.
He said: "The fans will have a chance to get used to it as well as the players.
"You won't recreate the Parkhead atmosphere, you are not going to fill Murrayfield in these early rounds.
"But it will be interesting to see what the crowd is. It is part of the season ticket so we will see how many turn up.
"Obviously everyone wants to see a good crowd for what is an important match.
"If the opposition had been better, that might have had an effect on the crowd.
"I think the 25,000 mark is the kind of crowd we should be anticipating.
"But Celtic are laying on reduced priced transport from Glasgow which is good and will hopefully allow as many people as possible to make the game."