Norman, who twice lifted the Claret Jug and lost out in a play-off at Troon in 1989, made headlines earlier this month when he attended the Masters after apparently buying a ticket on the secondary market.
The 69-year-old Australian was not invited by the R&A to compete in the Celebration of Champions or attend the Champions' Dinner ahead of the 150th Open at St Andrews, which took place just weeks after the inaugural LIV Golf event in Hemel Hempstead.
This year's championship from July 18-21 has sold out, ensuring a venue-record attendance of 250,000, and R&A officials were asked if Norman's name was on the list at their annual media briefing.
The R&A's director of corporate communications Mike Woodcock told the Scotsman: "I don't think there's a G Norman and I think someone would have let me know if there was.
"So, I'm not aware that he's bought a ticket so far. Obviously there's still tickets available on the resale platform and hospitality packages as well."
A total attendance of 250,000 represents an increase of 77,000 from 2016, when Henrik Stenson came out on top in a thrilling duel with Phil Mickelson.
"It is a big increase and I think there's been a huge amount done to try and make sure that the number we bring in is what the golf course can accommodate," Woodcock added.
"There's been a lot of work done in the on-course areas to ensure that the fans can get around and enjoy good viewing areas. I think the viewing decks, grandstand seatings and so on that we've put in can accommodate it."
Nine new tees have been created to lengthen the course by 195 yards to 7,385, with the par-five sixth extended to 623 yards.
The longest hole in Open history will be followed two holes later by the shortest, with an option for the "Postage Stamp" to play at 99 yards from a forward tee to a front pin.
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