The Italian Rugby Federation (FIR) revoked the franchise's license to compete in the competition last week, citing the club's mounting debts as the primary cause for ending it's two year existence.
While the FIR simultaneously stated their intent to enter a replacement team into the RaboDirect PRO12 next season, official details of where it might be based have not been forthcoming.
Geldenhuys' 30 Test caps for Italy coupled with an abrasive playing style would make him an attractive proposition for rival European clubs.
But regardless of where he ends up playing next year, he admits the current uncertainty surrounding the club occupies his thoughts.
"It came as a shock, definitely," said Geldenhuys, who has been playing in Italy since 2005.
"None of the players were expecting the club to just be taken away in the manner it has, a lot of the coaching staff didn't know about it either.
"All the players are trying to get their agents involved now to get something sorted.
"But with the way European club contracts work it's really, really difficult to find a different club before the start of next season.
"Originally Aironi was a four year plan and it's sad that all the hard work we have done will end here.
"We are still a new team and if we bring on a few more youngsters and get a few new guys as well, we could have done very well next season.
"When you compare this season to our first one we've improved a great deal.
"We haven't been pushed over once at home this year, except for in the Heineken Cup, but last year that happened a few times."
This term they have already recorded four victories, all at home, including a 21-17 win over the champions Munster.
The up-turn in their fortunes has coincided with Italy avoiding the Wooden Spoon in the Six Nations for the first time since 2007, with Geldenhuys playing in all five of Italy's games.
And the South African-born lock believes Aironi's demise will adversely affect the national team's future prospects, unless a replacement franchise takes on their playing staff en masse.
"A lot of youngsters have shown what they're made of this season," added Geldenhuys.
"We've struggled at tighthead all year but this weekend against the Scarlets Lorenzo Romano really stood up in the scrums and we got a penalty try.
"He is only 23 and players like him have got used to tough games in the PRO12.
"As long as there is another Italian team in the league it won't affect the national team but if those guys have to go and play in the Super 10 instead it will do some harm.
"As players we just want to know what is going on as it's hard to make a decision with the current situation.
"There are so many negative things happening off the pitch so the players have decided to focus on pulling off results on the pitch and we've got a great opportunity to do that against Connacht on Saturday."