Eugene, which has close ties to American sportswear giant Nike, won the right to host the biennial event despite the absence of a formal bidding procedure.
The BBC last month published an email from a senior Nike executive that suggested Coe had lobbied his predecessor Lamine Diack for the championships to be awarded to Eugene, which Coe denies.
Coe subsequently stepped down as a Nike ambassador, but he defended the process that saw the event awarded to Eugene, telling BBC Radio 4: "We have selected cities before not within a bidding cycle.
"My council decided that for the forseeable future, this was the best opportunity to get the World Athletics Championships into the United States.
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"Every sport is falling over itself to get into the largest sports market in the world."
A judicial source revealed on Wednesday that French prosecutors are looking at the decision by the IAAF (International Association of Athletics Federations) to award the 2021 championships to Eugene.
The preliminary investigation is understood to be looking at the various suspicions raised by the British media and to make sure that the French courts have jurisdiction.
Prior to succeeding Diack in August, Coe spent eight years working as IAAF vice-president, but said that deals could have been made during that time of which senior figures within the organisation were unaware.
"(The IAAF's conduct under Diack) is now a matter of police investigation and I can't maintain a running commentary on that," he said.
"If that has happened, that will take its normal course and people will be prosecuted."
Coe acknowledged that the allegations facing Diack and other senior IAAF figures were "abhorrent", but rejected the suggestion the affair was comparable to the corruption scandal plaguing world football governing body FIFA.
"We're talking about a criminal investigation, which is looking at a handful of people. That's of no comfort to me.