The draw for the group stage is made next Friday, with the Hoops set to be back in alongside the continent's elite clubs for the first time since 2017 after being eliminated in the qualifying rounds in recent years.
"We're really looking forward to the Champions League," said McGregor. "The play-off games are getting close to a conclusion and the draw will be after that.
"We're focused on looking after the league business - the here and now - but in the back of our heads we know the Champions League is coming around pretty quickly.
"We've played quite a few big teams but probably the one most of the Celtic fans would like is Real Madrid. I've not played against them yet but we know anybody we get drawn against will be a top team and a big challenge for us."
McGregor believes Celtic have benefitted from not having to play early-season qualifying rounds this summer as a result of Scotland's improving coefficient.
"It's definitely been a slower start to the season in terms of the number of games we've played but it's also given us good time to train and prepare really well for the games we have had," said the midfielder.
"You can see from the start we've had that the boys are working hard, they look fit and the team looks pretty cohesive."
McGregor was speaking on Wednesday after it was announced that Celtic are releasing a book called The Making of a Celtic Captain - the Callum McGregor Story which will relive the skipper's journey from his early years at the club to the present day.
"It's nice," he said. "The club came and asked me to do it and it's obviously a nice thing, recognising the career I've had up to now.
"I've enjoyed doing it. It forces you to look back a little bit and remember some of the things you've done in terms of your journey. It's been a nice little look back to the past.
"There are probably quite a lot (of standout moments) when I look back but I think lifting the (cinch Premiership) trophy as captain for the first time (last season) is probably the standout.
"I've had some pretty good ones. I've been a really fortunate boy to have so many highs so far in my career but I think that one probably just pips the rest."