Fiesta Bowl officials are likely to draw on their Big 12 ties as they set the matchup for this year’s game.

“It’s very important,” Fiesta Bowl president and CEO John Junker said Thursday from San Antonio, where he will attend the Big 12 championship game. “The Big 12 is our conference. We have a tremendous relationship.”

That means either Oklahoma or Kansas could be headed to Glendale, Ariz., for the Jan. 2 game, which is part of college football’s Bowl Championship Series. The Fiesta, Sugar, Orange and Rose Bowls will make their selections on Sunday, after the pairing for the BCS title game is announced.

If Oklahoma defeats Missouri in the Big 12 championship Saturday night, the Sooners would draw an automatic Fiesta berth as the conference champion.

A Missouri win would make things more complicated. The Tigers would head for the BCS title game, and the Fiesta would have first choice to replace them.

That’s where the 11-1 Jayhawks enter the picture. The Fiesta is expected to choose the Jayhawks, ranked fifth in the BCS, over No. 4 Georgia.

Kansas has had relatively little success in football. But its followers are excited about this season and would likely flock to Arizona for the game.

“Kansas looks like a team a lot of people would be excited (for) in a BCS bowl,” Junker said.

An Oklahoma-Kansas game isn’t out of the question, either. The Big 12 rivals did not meet during the regular season.

Arizona State also will receive strong consideration if it defeats arch rival Arizona to finish 10-2. The Sun Devils would be Rose Bowl-bound if they defeat Arizona and USC loses to UCLA.

The Fiesta was founded in 1971 to provide a bowl destination for the Sun Devils, who played in the lightly regarded Western Athletic Conference. But the Fiesta Bowl has handed out bids on merit for most of the last three decades, and ASU hasn’t played in the game since 1983.

“There’s certainly some sentiment expressed on behalf of Arizona State,” said Junker, an ASU alumnus. “They’ve had a good season that they can finish off with a victory over their rival.”

If ASU loses, the scenario becomes cloudier, with Illinois and perhaps Hawaii entering the picture. The Warriors won’t be eligible for a BCS berth unless they defeat Washington on Saturday.

“There’s a lot of potential alternatives that will excite some people and disappoint others,” Junker said. “One thing we’ve learned is never anticipate any of the outcomes.”