The 16 Regional sites were announced Sunday afternoon, and Norman was not among them.
OU played a pair of games against the TCU Horned Frogs this season and won them both.
The first one, in Norman, was a blowout victory for the Sooners, who scored two runs in the first, three in the third, three in the sixth, one in the seventh and four in the eighth en route to a 13-6 win.
OU even led 13-2 heading into the ninth inning in that one.
When the two met again in Fort Worth, it was a much different game, but again the Sooners came out on top.
They had a 4-3 lead after four, built onto it and hung on for a 7-4 victory.
As for Rice, the Sooners haven't played them since the Houston College Classic back in February 2008, and that one was all Rice.
The Owls won 7-2 as they racked up 12 hits and OU had three errors in the contest.
Prior to that, the Sooners took on the then-No. 1 Owls in the 2006 Super Regionals in Houston and had a 4-3 lead in the sixth inning of the rubber match game but fell short in a 9-5 defeat.
One other location that could play host to the Sooners in 2011 is Los Angeles, Calif., where the UCLA Bruins will have a regional.
If OU travels there, it'll likely be the No. 1 seed.
The Sooners played the Bruins in last year's Whataburger Classic at Whataburger Field in Corpus Christi, Texas, and dropped a 5-2 decision.
A year earlier, OU swept UCLA out of Norman.
As for those teams and the overall course of their seasons, TCU won the Mountain West Title in the regular season but fell short with a 2-2 showing at the MWC Tournament, still comprising a 42-18 record.
They have been in the Top 10 throughout the season coming off their College World Series appearance last year.
The Owls tied with Southern Miss at 16-8 for the Conference USA regular season title and then won the C-USA Tourney over Houston Saturday night.
They are 41-19 and listed near the Top 15 but figure to easily be in there in next week's polls.
UCLA, the Pac-10 champion, is hovering right around the Top 20 in the most recent edition of the polls.
They just took the first two games of a three-game series in Tempe, Ariz. against the Arizona State Sun Devils and have a 33-21 overall record.
It should be noted that OU won't play any of these teams in the first game as one will be the No. 1 seed and the other will be the No. 2 seed, but the two will likely battle for the regional championship.
The Sooners will find out for sure just where they're going during the Selection Show at 11:30 a.m. Monday.