In the wake of the World Anti-Doping Agency commission which reported widespread, state-backed doping of Russian athletes, former decathlete Thompson said his friend and fellow double Olympic champion Coe had been presented with the "defining moment" of his IAAF presidency.
On Friday, the IAAF Council meet in Monaco to consider sanctions against the Russian athletics federation after a recommendation from the commission that it be suspended.
"What the whole situation needs is for its leader -- and Seb Coe is the custodian of what I think is the greatest sport in the world -- to stand up and show some leadership," Thompson told Talksport radio.
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"He needs to let the people know, he needs to let the cheats know, and he needs to make sure all the other federations understand there are serious consequences to this. I reckon he needs to make some examples (of the cheats).
"He has the best interests of the sport in his heart. He cares about it passionately and he wants to see it thrive. I don't think he will allow this situation to continue.
"He has to stand up and make some proper decisions, but not in a back-door diplomacy way. He needs to be upfront and let the public see what he's doing.
"If that means more and more bad things come out, then so be it. Let's clear the decks and start again. This is going to be the defining moment of his presidency."
(Writing by Ian Chadband)
