The Englishman picked up a groin complaint during Sunday's 3-1 Scottish Cup semi-final win over Livingston and Bhoys boss Martin O'Neill admitted he was doubtful for the trip to Spain.
Sutton, who scored twice against Livingston, is ready to play through the pain barrier and insists he would "walk through a brick wall" to play.
"It's a bit sore," said Sutton. "I have had a problem the last two weeks but we will wait and see how it goes and hopefully it will settle down.
"I will rest it and see on Wednesday. I've had it a while but I have always managed to get through games.
"I have not been having injections. It is a bit too high to put a jag up there. I would walk through a brick wall to play.
"It was not very good in the second half and I came off as a precaution but I have come through these games. It has been sore but if you are fit you can get through.
"I can't look too far ahead but I want to play every game even though there are three games a week.
"I want to be involved in all the games at this stage of the season. It is not ideal to play three games a week but I want to play.
"People complain about the number of games but you would rather be involved in three competitions than nothing. I want to win as much as I can."
Villarreal have an injury worry of their own after Spanish striker Jose Mari picked up a rib injury in Sunday's defeat to Deportivo La Coruna.
The former Milan striker will be given every chance to prove his fitness ahead of the game on Wednesday.
Meanwhile, Celtic chairman Brian Quinn has handed O'Neill an extra incentive to progress in Europe by revealing some revenue will be made available to strengthen the squad.
O'Neill has called on the club's board to allow him to spend some money with Henrik Larsson set to leave and Quinn is set to grant the Northern Irishman's wishes.
"The further we go in the Uefa Cup and in domestic competitions, then the more revenue we generate," said Quinn.
"He will certainly get some part of the initial revenue - we have said that to him already - and we will stand by that."
