The Ayrshire venue has not hosted a full international since the visit of Wales in a friendly in May 1997.
Last night's win over Estonia was held at Pittodrie, while Easter Road was used earlier in the season for the visit of Australia.
Shiels said: "I would like to see an international match at Kilmarnock.
"My chairman has had the foresight to work on the pitch and spend a lot of money on it.
"Outside of Glasgow, it's probably one of the best facilities to have an international match.
"We've got great facilities and we've a hotel on site, which is fantastic.
"We would be more than willing for the SFA to avail of that service.
"It's a fantastic set-up and they have to realise that we are a football club as well.
"I'm disappointed we have been overlooked yet again."
Meanwhile, Cillian Sheridan could be out of action for up to six weeks with a hamstring injury sustained during last week's William Hill Scottish Cup tie against Inverness.
Ross Barbour is also set to miss this weekend's visit of Motherwell with a flu bug.
Shiels said: "It's a blow. We've potentially lost two more.
"It's not an easy game. Motherwell are flying high so it's going to be tough for us."