Lord Coe believes both London and Doha are focusing on their battle for the 2017 World Championships despite reports one of them may be awarded the 2019 event.
An announcement on 2017 will be made on Friday and Lord Coe said there had been "no formal discussions" around 2019.
Discussing a possible double decision, he said: "I wouldn't rubbish it.
"When you are at this stage of a bidding process the speculation and gossip changes all the time."
But the International Association of Athletics Federations (IAAF) vice-president added: "It was not raised in the council and there has not been any formal conversation with any bid teams.
"We have just drawn lots and been told the order of presentations on Friday so we should assume this is the process we are locked into."
London and Doha are going head-to-head for the 2017 event. But some reports have claimed the IAAF may announce successive hosts for the first time with London getting 2017 and Doha 2019.
However Doha officials are also understood to much prefer 2017 as they would be concerned that having a 2019 championships could conflict with their bid for the 2020 Olympics.
Coe said: "The very firm instinct for both bids is that it is 2017 we are bidding for and, in London's terms, 2017 is what we are able to deliver on and that's our focus."
The London 2012 chairman would not be drawn on London's chances, saying the campaigning had to go on to the last minute.
He added: "I can tell you our case is being heard very sympathetically. These are my colleagues - it is not selling a second-hand car to someone you have never met.
"These are friends and colleagues, people I have known for 30 years, and they know the strength of our case."
Earlier on Wednesday, UK Athletics chairman Ed Warner had said: "From London's perspective we are in no position to accept 2019 if we were offered it.
"We have a coalition of funding partners and it would take many months, perhaps stretching beyond a year, to get an answer and we could not guarantee to the IAAF we would accept.
"We are in Monaco for the 2017 pitch and we sincerely hope we win it."
UK Sport, the government, the London mayor and UK Athletics have all agreed to contribute to the funding.
