Cope, a former British Cycling employee who denies any misconduct, said he had not yet been officially summoned by the Culture, Media and Sport select committee, which will also question UK Anti-Doping (UKAD) head Nicole Sapstead on Feb. 22.
"I want to clear it up because I'm fed up with my name being dragged through the mud," Cope told British media. "To this day, hand on heart, on my kids' hearts, I do not know what was in there. I was asked to do a job.
"I was told by senior management, 'We want you to do that' or, "Do this'... People say, 'You're naive, you should have asked because you're going through customs'. Maybe I was, but also why would I question?
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"I had been working at British Cycling for eight years and I had never seen anything to question."
Cycling has been rocked by revelations that a mysterious jiffy bag containing medication was transported to France by British Cycling women's team manager Cope for Wiggins and Team Sky at the 2011 race.
Team Sky's use of Therapeutic Use Exemptions (TUEs) has also been under investigation after cyber-hacking website Fancy Bears leaked medical information held by the World Anti-Doping Agency (WADA) on Wiggins and former team mate Chris Froome.
Neither rider is suspected of any wrongdoing.
Team Sky boss Dave Brailsford has also already given evidence to the select committee, saying in December that the "mystery" delivery reported in a Daily Mail story was WADA-approved decongestant Fluimucil.
(Reporting by Simon Jennings in Bengaluru; Editing by John O'Brien)
