Bettison worked in the West Yorkshire Police force at the time of the 1989 tragedy, which resulted in the death of 96 Liverpool fans, and was later revealed to be part of the authorities' attempts to place blame onto the supporters.
Following Wolves' away clash with Bradford City on Saturday, a number of photos have emerged of Morgan shaking the hand of Bettison, sparking outrage among Liverpool fans.
The League One club has now confirmed that Bettison was invited to the game by Morgan, who is a lifelong Liverpool supporter.
A statement from Wolves said: "The club has been contacted by many fans regarding some Express & Star tweets this morning referring to a big Wolves story, which was about to break.
"The story is that Sir Norman Bettison attended the Bradford City away game in the same way he has attended many Wolves games in the past.
"Steve Morgan and Sir Norman Bettison have known each other for many years. Everyone connected with the club has the utmost sympathy and respect for the victims of Hillsborough and their families, and today's Express & Star story should in no way should detract from those heartfelt sentiments."
Fresh inquests into the disaster are expected to be carried out in March next year after the families of the victims successfully campaign to have the original 'accidental' verdict quashed.