David Brailsford is due to appear in front of a parliamentary select committee on December 19, where Cookson hopes that the Team Sky boss will be fully transparent about the contents of the package.
“I would hope that there is full disclosure to the select committee,” Cookson said in an interview with The Times.
“I am surprised that one particular package has been singled out and I don’t understand why that should be, unless there is someone who has leaked this [and] presumably has some sort of reason to suspect that there is something in it that they would rather not go into public.”
“I don’t understand why there is a mystery about it, to be quite honest. One would imagine there is a record of this.”
Wiggins and Team Sky have come into fire in recent months, first over revelations that Wiggins received a therapeutic use exemption (TUE) that allowed him to use otherwise illegal corticosteroids on medical grounds before the 2011 and 2012 Tours de France and the 2013 Giro d’Italia, and then over the mysterious medical package that was delivered to the team at the 2011 Critérium du Dauphiné.
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Simon Cope, then a British Cycling staff member, flew with a package from Great Britain to Geneva, Switzerland, and drove it to the team in France.
He met Sky medic Dr Richard Freeman at La Toussuire ski resort, on the final stage of the Critérium du Dauphiné on June 12.
Wiggins won the French stage race, which set him up for a run at the Tour de France. He abandoned the Tour due to a broken collarbone, but returned in 2012 to become the first British winner.
Brailsford said that he knows what was in the package but would not reveal its contents. It is unknown if it was for Wiggins or another of Sky’s other riders at the race.
Brian Cookson was British Cycling president at the time of the incident, but was adamant in his answer when questioned over whether he was aware of the contents of the package.
“No, absolutely not, but I’m not surprised that packages are taken and delivered to teams from time to time, whether pedals, shoes, medical products, I’m sure that’s happening all the time with all the teams because they are always on the road.”
Away from Brailsford’s appearance in front of the select committee, UK Anti-Doping has also been investigating the package.
However, the report is expected to clear Wiggins of any wrongdoing, although Team Sky and British Cycling are expected to come under fire.