Sepp Blatter recently admitted that he may have made a mistake in awarding the major tournament to the Arab state, which would force nations to compete in temperatures of up to 50 degrees if taken place in the traditional summer months.
However, Carragher believes that the World Cup should be played at the end of the Premier League season but in a different country.
"It raised eyebrows when we saw that the World Cup was going there," Carragher told Sky Sports News. "Is it a 'mistake'? Is that being disrespectful to Qatar? I don't think it's ideal to be playing a World Cup in those conditions.
"So now people are talking about a winter World Cup, but how does that affect the Champions League, the Premier League, La Liga, the Bundesliga and all of the leagues around Europe? For me, a World Cup is at the end of a season in the summer. If FIFA have messed up and the conditions aren't right then I think you have to look at it again and give it to somewhere else.
"You can't be messing about with all the leagues in Europe and how it's set up. It's been this way for so long. If they've made a mistake I think they've got to rectify it."
The FIFA Executive Committee will vote on whether to move World Cup to the winter months this October.