Francis's statement contradicts an interview Peter Karmanos, the former owner of the Hurricanes, gave with Geoff Baker of The Seattle Times on Thursday.
The Flames were on a road trip when the controversy broke. For that reason, the Hall of Famer said it would have been inappropriate to comment on Peters while another team - the Flames - conducted an investigation into Peters' past conduct.
The NHL is also investigating. Francis also said that he will not comment on the matter further.
Calgary hosts the Ottawa Senators on Saturday night.
Jordan, 29, wrote on Twitter that Peters once kicked him in the back during a game and punched a different Carolina skater in the head, an account that current Hurricanes head coach Rob Brind'Amour corroborated to the media on November 27. "I took immediate action to address the matter and briefed ownership", said Francis, who is now the GM of the as-yet unnamed expansion team in Seattle. "To my knowledge, no further such incidents occurred".
Other players corroborated Aliu's claims and additional complaints and gripes against Peters from his time as the head coach of the Carolina Hurricanes surfaced as well.
Both Peters and Francis left the Hurricanes organization in a matter of days in April 2018 when Dundon asserted control over the team.
Francis extended Peters' contract in July 2016 through the 2018-19 season. Peters resigned after the 2017-18 season, having failed to reach the Stanley Cup playoffs in any of his four seasons.
"To me, it's what happened after that I'm proud about actually, the way the players handled it, and the way the support staff handled it, which was to bring it to management right away", Brind'Amour said. He gave Peters a contract extension after the 2015-16 campaign - Jordan's last National Hockey League season.
Karmanos sold majority interest in the Hurricanes to Tom Dundon in January 2018 but remains a minority owner.
In more than 30 years at The N&O, Chip Alexander has covered the N.C. State, UNC, Duke and East Carolina beats, and now is in his 11th season on the Carolina Hurricanes beat.