The 17-year-old from Shamrock Rovers has scored nine goals this season, becoming the youngest ever scorer in the Conference League at 16 years and 197 days.
He netted against Molde in the competition to break the record.
The forward scored three goals in five games for the Republic of Ireland as they made it to the last 16 of the under-17s World Cup, and has since been capped at under-21s level.
Noonan is catching the eye of several clubs, including Manchester United and Manchester City, but the Irish Sun reports that Celtic are confident of being at the front of the queue to sign him.
He is said to be keen on a move to the Scottish champions.
The Parkhead club could potentially sign him in January and then loan him back to Rovers, where Johnny Kenny previously thrived on loan.
Noonan only moved to Shamrock from St Patrick's Athletic last year, believing he would get more first team football, and he has had a breakthrough year.
Manchester City have held a long-term interest but city rivals United are also now thought to be in the hunt.
He was nominated for PFA Ireland Young Player of the Year while winning his club's Young Player of the Year award.