The 39-year-old will pass the 145-game record that he currently shares with former Real Madrid striker Raul if he plays against Shakhtar Donetsk on Wednesday night.
When made aware of the statistics, Giggs told the club's official website: "Really? Wow. I didn't know that. It's a great competition and I've been lucky enough to win it twice and play a lot of memorable matches.
"There have been so many great players to have graced the tournament and Raul is up there as one of the very best - he has a great goalscoring record and he's won it three times. If I do pass him, it will be a great source of pride for me."
Giggs lifted the Champions League trophy with United in 1999 and 2008.