The comments by the head of Fifa's auditing and compliance committee came as bribery claims mounted against disgraced former Fifa vice president Jack Warner, the man at the heart of the scandal engulfing football's world body.
"If evidence exists that Qatar and Russia received the (World Cup) awards only thanks to bribes, then the awards could be annulled," Domenico Scala told the Swiss newspaper Sonntagszeitung.
He said however that "this evidence has not been provided" so far.
His comments are the first by a senior Fifa official to even open up the possibility of either Russia or Qatar being stripped of the right to host the football extravaganza.
Swiss judicial authorities are already probing the awarding of the 2018 and 2022 World Cups to Russia and Qatar as part of a far-reaching corruption scandal that has also raised questions about the 2010 event in South Africa.
Around 14 current or former Fifa officials and sports marketing executives are also accused by US prosecutors of taking part in a sweeping kickbacks scheme going back 20 years involving a total of $150 million in bribes.
The revelations have thrown the world of football into turmoil and led to the resignation of long-serving Fifa president Sepp Blatter last week, just four days after his reelection for a fifth successive term.
Blatter's replacement will not be chosen for months, but Freddy Rumo, a former vice-president of European football's governing body Uefa, has said that changing Fifa presidents will not root out graft at the organization.
"The corruption, in my opinion, has nothing to do with Blatter's person," he told Swiss public broadcaster RTS.
"The solution of replacing a president with another will have basically zero effect."
Although Blatter has not been charged and has denied any wrongdoing, allegations are swirling around his one-time right-hand man Warner.
Accusations surfaced on Sunday that Warner sought a $7 million bribe from Egypt for votes in the bidding process for the 2010 World Cup, and that he pocketed a $10 million payment from South Africa -- the eventual host.
Warner was arrested on May 29th at the request of US authorities and is currently free on $400,000 bail pending a decision in his extradition case.
The 72-year-old former schoolteacher and Trinidadian justice minister has denied all the allegations against him.
The BBC claimed he personally used the $10 million payment to Fifa in 2008, which South Africa says was intended for football development for the African diaspora in the Caribbean, where Warner was the longtime football baron.
The BBC, citing documents it has seen, said Warner laundered the money through a supermarket chain, made cash withdrawals, paid off his credit cards and took personal loans.
In three transactions in 2008, funds totalling $10 million were moved from Fifa's bank into an account of the Confederation of North, Central American and Caribbean Association Football (Concacaf) which was controlled by Warner, then its president.
According to a 2007 email published on Sunday by South Africa's Sunday Times, Blatter and then South African president Thabo Mbeki discussed the $10 million.
The email came from Fifa secretary general Jérôme Valcke, who has previously said "I have nothing to blame myself for" over the payment.
'$1 million per vote'
In another allegation, former Egyptian sports minister Aley Eddine Helal said Warner asked Egypt in 2004 for a $7-million bribe in exchange for seven votes to host the 2010 Cup.
"Warner was the one who approached us from Fifa. He said he could guarantee us seven votes . . . he asked for $1 million for each vote," claimed Helal, who has said Warner's offer was rebuffed.
Egypt, one of the countries dominating African football, received no votes in the 2004 Fifa ballot.
Warner — still a powerful member of parliament in Trinidad and Tobago — has taken out paid advertisements in the Trinidadian media, published articles in local newspapers and held rallies with his Independent Liberal Party to defend himself.
The country's justice minister said on Sunday that Warner should be investigated locally, but added that he should nevertheless turn himself in to US authorities.
Fifa has also been rocked by testimony from disgraced former North American football supremo Chuck Blazer that he and other Fifa executives agreed to accept bribes during bidding for both the 2010 Cup and the 1998 event hosted by France.
Blazer's testimony — released last week — is a key plank in the US probe against Fifa, which federal prosecutors are pursuing as a "racketeering influenced corrupt organization".
South Africa on Sunday "categorically" denied it paid bribes to secure the World Cup — the first in Africa and one of Blatter's main pledges when he took over as Fifa president in 1998.
The former chief of France's 1998 World Cup organizing committee last week also denied any "irregularities" over their bid.