Ruud battled to a four-set win in the previous Paris meeting between the pair at the same stage last year and exchanged a tense handshake at the net with his opponent, but the drama intensified off the court.
He accused Rune of lying after the youngster said that the world number four shouted "ja" (yes) in his face in the locker room following the match, but the duo appear to have put their differences behind them.
There was a warmer handshake after Rune rallied to beat Ruud in the Italian Open semi-finals last month, his first victory over the Norwegian in five meetings.
"Obviously there was drama last year and I hope we can make less drama this year," said Rune, who laboured into the quarter-finals with a five-set victory over Argentine Francisco Cerundolo.
"We played in Rome. It was a good match. He's a good player. I respect him. There's no problem. We're good. Should be a match without problems, hopefully. Looking forward for it.
"I lost last year. It's going to be the same scenario... Hopefully, I can turn it around and make it different this year."
Last year's runner-up Ruud has eased into the last eight dropping only two sets in his four matches, having put his thrashing by Rafa Nadal in the 2022 final behind him.
He will aim to capitalise on the 14-times champion's absence this year due to injury and continue pushing for a maiden major, as will Alexander Zverev after the German romped to a 6-1 6-4 6-3 win over Grigor Dimitrov.
Zverev will play surprise package Tomas Martin Etcheverry for a place in the semi-finals, the stage at which he suffered a serious ankle injury last year.
Can anyone stop Swiatek?
In the women's quarter-finals, holder Iga Swiatek will face a rematch of the 2022 final against American Coco Gauff.
Beatriz Haddad Maia - the first Brazilian woman in 55 years to reach the quarter-finals at a Grand Slam - will then take on another history-maker in Tunisian Ons Jabeur.
Jabeur became the first African player to reach the last eight at each of the four majors in the Open Era and can inch closer to a first Grand Slam title after losing the Wimbledon and US Open finals last year.
