Jonathan Tiernan-Locke, who rode for Team Sky until he was sacked for a doping violation in 2014, was asked about Wiggins' use of the anti-inflammatory drug in a BBC interview.
"I don't want to insinuate anything but the timing doesn't look great," Tiernan-Locke said.
"You assume if you had a need for such a thing it would be consistent throughout his career, that you'd use it year in year out, so from that point of view it looks suspicious."
Wiggins' use of TUEs, which allow athletes to take banned substances for verified medical needs and are signed off by sports federations, was leaked last month by the Russian-based Fancy Bears cyber hacking site.
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There is no suggestion of any wrongdoing on the part of five-times Olympic gold medal winner Wiggins who denied looking for any "unfair advantage", saying the medication was to reduce the impact of asthma and allergies.
Team Sky boss Dave Brailsford also defended Wiggins by saying he had suffered from allergies for as long as he had known him and that the team had not "crossed the line".
Tiernan-Locke said that while Sky would have been thorough in their preparation for the Tour de France, the way their use of TUEs was revealed had aroused suspicion.
"People I have spoken to, out of training, it has kind of tainted (Sky's) image somewhat," he said.
"I think their modus operandi was to put things out in the public domain and look transparent and not have anything to hide. It's somewhat less than transparent.
"From the other perspective we've got a guy who's favorite for the general classification in these big races, so for a team like Sky who are so thorough, they don't want to leave anything to chance, so why risk these allergies derailing their best-laid plans, so I understand it."
The data leak also showed Wiggins was given permission to take triamcinolone before the 2011 Tour de France and 2013 Tour of Italy.
On each occasion the TUE was approved by British authorities and cycling's governing body the UCI.
(Reporting by Martyn Herman; Editing by Tony Jimenez)
