The American sprinter, who was provisionally suspended earlier this month, risks a two-year ban that would rule him out of next year’s Tokyo Olympics.
The 24-year-old said in a statement on Twitter that he was the victim of “a purposeful attempt to get me to miss a test” in December last year.
He said he was out shopping for Christmas presents and had not received a phone call.
The Athletics Integrity Unit (AIU), the anti-doping arm of World Athletics, said “a phone call is discretionary and not a mandatory requirement”.
“It’s not really our policy to comment on unresolved cases — this is now quite properly a matter for the AIU,” Coe told BBC Sport.
But he added it was “not a good story (for athletics)”.
“No athlete should minimise the importance of the whereabouts rule,” said Coe.
“The whereabouts rule is to protect the athletes, it’s to protect their reputations and it’s to make sure that we move as hard and as fast as we can to drug-free sport.
“It’s one hour a day — this is not arcane maritime law, this is not complicated.
“The vast majority of athletes make sure they don’t miss those tests. They have to take it seriously.”
Coleman, who clocked 9.76sec to win 100m gold in Doha in September 2019 said he had never taken drugs.