Qatar was chosen to host the World Cup but temperatures can reach 50 degrees Celsius (122 degrees Fahrenheit) in the desert state during the summer, leading to calls to switch it to earlier in the year.
However, that would have severe consequences for the world's biggest domestic leagues such as the Premier League which has already voiced fears over a winter World Cup.
"My end view is either that it should be left where it is or there should be a re-bidding process," Bernstein, whose successor Greg Dyke described a summer tournament in Qatar as 'impossible', told the BBC.
"It was a strange award in the first place, we all know that."
Bernstein said he was against the idea of the tournament being moved as Qatar won the right to host the World Cup on the basis of a summer bid, using air-conditioned stadia.
"My personal view on this is unchanged. In 2010 FIFA awarded two World Cups at the same time. It was a controversial thing to do and I believe that FIFA regret doing it now," he said.
"Bidding for a World Cup is a serious business. There is a lot of money and national prestige involved.
"The bid that Qatar submitted was a summer bid. It was accepted by FIFA as a summer bid so I don't believe that it is impossible to hold the competition in the summer.
"It may be undesirable, with fans coming out of cool stadia into boiling heat clearly an issue," he added.
"But I think the idea of just arbitrarily changing from summer to winter smacks of what I would call a false prospectus."
Qatar beat bids from South Korea, Japan, Australia and the United States. Russia will host the 2018 World Cup.