The 20-year-old midfielder, who made the pre-contract move from Sheffield Wednesday earlier this year, could well face his former teammates in a pre-season friendly at a training facility in South Wales on Wednesday.
It will be an interesting experience for Shaw and fellow Parkhead new boy Osaze Urhoghide, who has also made the switch from Hillsborough.
Asked whether his former teammates have been in touch ahead of the fixture, Shaw said: “There have been a few words!
“It is going to be weird to be honest, my first game for Celtic playing against Wednesday but it is just like any other game of football. When you're on the pitch, you don't really think about it and you just think about winning.
“I am looking forward to it.”
The match will also be the first in the dugout for new Celtic boss Ange Postecoglou and Shaw reckons it will be a good first test as the Hoops begin preparations for the all-important Champions League qualifier against Danish side FC Midtjylland in a fortnight.
“It will be a tough game,” Shaw added. "It won't be easy at all. They [Wednesday] have got a lot of good players still there.
“Obviously I know all the lads really well and they know how I play. It will be nice to see a few familiar faces. I will go in and give it 100 per cent and we will see how it goes.
“We have to play our football and play the way we want to play and not worry about any other team.”