UK Anti-Doping has been investigating whether triamcinolone, a banned corticosteroid, was in that package since last September but has been unable to find any evidence to either prove or disprove the claim.
Confirmation there is no anti-doping case to answer is understood to be coming soon after the general election on June 8, although Team Sky and the sport's governing body British Cycling will be censured for their medical record-keeping.
This, however, will come as a relief to Dr Richard Freeman, the medic involved, as well as the team and its then star rider, Sir Bradley Wiggins.
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They have repeatedly denied any wrongdoing and have said the package contained Fluimucil, a legal decongestant Freeman claims he administered to Wiggins via a nebuliser.
The reputations of all concerned, however, have been damaged, particularly as it was revealed in September by Russian computer hackers that Wiggins had injections of triamcinolone before his three biggest races in 2011, 2012 and 2013, including his 2012 Tour de France victory.
Those injections were legal as he received a special dispensation from the anti-doping rules, known as a therapeutic use exemption (TUE), to treat a pollen allergy.
Hamilton, who helped Lance Armstrong to win his first three Tour de France titles before becoming one of his main rivals, said he did not know the facts of Wiggins' case but was well aware of the drug.
Now 46, Hamilton won stages in cycling's three grand tours, became the only American to win one of the sport's five biggest one-day races, finished second in the 2002 Giro and fourth in the 2003 Tour.
His biggest achievement was victory in the time trial at the 2004 Olympics but, having already failed tests in 2004 and 2009, he confessed to cheating throughout his career in 2011 and returned his gold medal.
Speaking to Press Association Sport at the Sport Resolutions conference in London, Hamilton said he and his team-mates "abused the crap out of" Kenacort, a brand of triamcinolone.
He said: " It helped you 'lean out' for the grand tours and it was very effective. Look at the pictures - I weighed 30 pounds less than I do now. Not healthy.
"The main guys on the team would get a TUE to cover the race and then top up during the race - it was like a free pass.
"But don't forget, we were also taking (blood-boosting drug) EPO and doing transfusions. That was the serious stuff.
"And there are legitimate reasons for using corticos and I don't know the facts of Brad's case. If cycling wants to address this they'll have to change the system and perhaps bring in a rule that you can't ride for two weeks after a shot."
Hamilton, who revealed his doping in a best-selling book in 2012, was speaking on the day it was revealed Italian riders Nicola Ruffoni and Stefano Pirazzi had tested positive for growth hormone ahead of this year's Giro d'Italia.
"The testing is better now, and they're doing more of it, but there's still doping in cycling," said Hamilton.
"We're still catching cheats and there are quite a few under the radar. And doping is in amateur cycling now, the under-23s and masters - it's not a pretty picture.
"But I'd much rather be a rider now than then, because I believe you can compete clean now.
"What makes me laugh, though, is this mentality that doping is all in the past. Was there a certain day when the peloton became clean? Was it 2006? Really?"
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