Asked whether FIFA's ethics committee would simply investigate David Triesman or the comments themselves, Valcke told a news conference: "Both."
Triesman quit as England's 2018 World Cup bid chief and FA chairman on Sunday after British newspaper the Mail on Sunday reported secretly recorded comments.
Triesman was quoted as saying that rival bidders Spain and Russia were conspiring to bribe referees at next month's World Cup in South Africa. The alleged comments badly damaged England's bid to host the 2018 or 2022 World Cup.
FIFA said on Monday that its ethics committee would investigate the comments.
"We are waiting for various statements...the ethics committee will decide which person they want to hear and which people they want to invite for a hearing," Valcke added.
"The ethics committee will make a report over the next days, we will do it as soon as we can and not waste any time," he added.
Valcke later told reporters: "I definitely want to have something before the World Cup because some of the comments were about the World Cup. It has to be quick.
"We are looking at the content of the allegations because it was about the World Cup and the bids and also on Lord Triesman and the way that he made those statements."
Triesman, 66, resigned from the bid team and the FA after little more than two years in the job.
PRIVATE CONVERSATION
In a statement, Triesman said that during a private conversation he had commentated on speculation circulating about conspiracies and never intended his remarks to be taken seriously.
Ex-FA chief Geoff Thompson is the new bid team chairman, with David Sheepshanks and Roger Burden appointed joint acting chairmen of the FA.
In an effort to limit the damage, the England 2018 team have sent letters of apology to their Spanish and Russian counterparts as well as FIFA.
"It would be strange if I said life wasn't a bit harder because of what's happened but hopefully we've dealt with what's happened quickly," Jonathan Hall, the FA's director of services, told reporters.
"We will carry on with our football business and that just simply has to go on."
