Wiggins, also a five-time Olympic gold medallist, told the BBC on Monday that he had "100 percent" not cheated but Sutton believes a more detailed response was needed.
"They need to explain it all to everybody," the Australian, who had a key coaching role at Team Sky from 2010-13, told Sky Sports.
Wiggins was granted a therapeutic use exemption (TUE) to take the corticosteroid Triamcinolone, which helps asthma sufferers, shortly before the 2011 Tour de France, his 2012 Tour win and the 2013 Giro d'Italia.
But the report, that received "confidential material from a well-placed and respected source" about Sky's medical policy from 2011-13, believes the 37-year-old may have been treated with Triamcinolone on up to nine occasions over four years.
Sutton wants Wiggins and Freeman to come forward and clear up the inconsistencies between what the DCMS committee heard about the frequency of the cyclist's use of the drug, compared to what the rider said himself on Monday.
"I cannot say I know a lot about Brad's use of it in or out of competition," Sutton, who gave evidence to the committee last year, said.
"I am told by the doctor he needs a TUE for this event etcetera etcetera. Outside of the event, you have to sit down and ask them. I am calling for him and the doctor to come forward and tell the truth.
"He is a sufferer, I have seen him suffer and gasping for breath after effort, I saw what he was going through, I cannot answer how often he used it. Only the doctor and him can tell us."
(This story has been refiled to fix typo in first paragraph)
(Reporting by Hardik Vyas in Bengaluru; Editing by John O'Brien)
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