Uefa president Michel Platini had already pledged to help Cardiff if they were to win the FA Cup and Gaillard confirmed that there is a lot of sympathy for the Welsh side within European football's governing body.
"From our point of view it would be sad if they win the FA Cup and cannot compete in Europe," he said.
"So we will be suggesting this to the executive committee. There is a lot of sympathy for Cardiff and I would expect it to go their way."
Gaillard also confirmed that no decision will be made before the final so Cardiff would not know their fate before facing Portsmouth.
The FA is considering its position on European qualification for the winners of the FA Cup
Prior to Sunday's semi-final, the FA had already said it would review the rule preventing Cardiff qualifying for Europe.
"The FA is considering its position on European qualification for the winners of the FA Cup," said a spokesman.
"Historically, the understanding of the FA has been that Welsh clubs were ineligible for the Uefa Cup should they win the FA Cup.
"The question of eligibility for Welsh clubs has not arisen for many years so it is only now appropriate for us to look at the issue afresh.
"At this time, there has been no definitive decision taken as far as this year's FA Cup is concerned.
"The FA has contacted Uefa and the Football Association of Wales [FAW] to ascertain their views. We are aware of the comments expressed by Uefa president Michel Platini this week."
Cardiff chairman Peter Ridsdale has also hinted the club would challenge the English FA's current rules and regulations.
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