Jim Boyce, from Northern Ireland, said the 54 Uefa associations agreed at a meeting in Croatia that the World Cup should not take place in the summer, when temperatures can reach 50 degrees Celsius.
However, they want Fifa to consult with the game's major stakeholders before making any decision about exactly when the tournament is staged.
Fifa's executive committee is now expected to agree in principle to move the World Cup to the winter at its meeting in Zurich on October 3 and 4.
Boyce said: "What has come out of this meeting, and what I think is sensible, is an agreement by the Uefa countries that the World Cup cannot be played in Qatar in the summer. Everyone was certainly in agreement about that.
"But what the 54 countries do not want Fifa to do is to make a decision yet on exactly when in the year it is going to be played. "There is still nine years to go and people feel Fifa should sit down with all the major stakeholders and come up with a solution that would cause the minimum disruption to football.
"There is plenty of time to do that in my opinion, and hopefully footballwill be the winner."
There could well be disagreements in the future however over whether it is played in January 2022 or November/December of that year.
The British associations told the meeting they want to make sure that the Christmas week is protected for domestic football, while Uefa chiefs favour January so that it would not impact on the Champions League.
Fifa are believed to favour November/December so that it does not clash with the winter Olympics.
The meeting saw the 54 European countries split into four groups to debate the issues surrounding moving the tournament in Qatar.
At least one of the groups, including the Scottish FA, suggested a possible start to the tournament as January 22, 2022, and Boyce said his personal preference would be for the end of January and February.
That however would bring Fifa into direct conflict with the powerful International Olympic Committee, who would not want any clash with the winter Olympics.
Other groups at the Dubrovnik meeting had different views on the best date to hold a winter tournament and Boyce said no overall decision was reached on that issue.
He added: "There has been no decision on whether it should be in January or another time. The European federations do not want Fifa to decide on the dates without consultation."
Last week, Fifa general secretary Jerome Valcke said Christmas matches would not be affected by any switch - and that there was no chance of moving the tournament from Qatar.
Valcke said: "We are not talking about taking Christmas or New Year away. Christmas is safe. The World Cup will not be played between December 24-January 1, so that will mean Boxing Day is safe.
"We are not talking about removing we are talking about moving, that's key. We are talking about moving [the tournament] in the year 2022 in the country which has been awarded the World Cup."
The Premier League has always opposed a switch and together with other European leagues has called for there to be no definitive decision next month and a full consultative process.