CHICAGO -- When you are as proactive in improving your baseball team into a World Series contender as White Sox general manager Ken Williams, you get used to hearing your name tied to rumors at this point of the season.

"You know how many times we've been sitting here and we [hear], 'Most likely it's the White Sox. They are going to do this, they are going to do that, the White Sox are involved in trade discussions with this guy, that guy,'" said Williams, holding court with the media prior to Saturday night's game against Cleveland. "And I'm sitting at home and I call [assistant general manager] Rick [Hahn] and I say, 'Hey, have you had conversations with team so and so? No, I haven't, so let's call [White Sox chairman] Jerry [Reinsdorf] to see if he had any.'"

Saturday's rumor, which actually took root on Friday night, centers on Toronto outfielder Alex Rios. According to ESPN.com, citing Major League Baseball sources, the White Sox are most likely to have placed a waiver claim on Rios.

Once the claim is made, the Blue Jays can let go of Rios, pull him back and keep him for the rest of the season or work out a trade with the team that put in the claim.

Teams are not allowed to comment on waiver claims, and Williams followed that rule on Saturday where any direct talk of Rios was concerned.

"Every day there are a ton of players that go through waivers from every team, and teams put a lot of guys through, not necessarily to try to trade them or try to move them, but more so to disguise some of the guys that they really want or are trying to move," Williams explained. "This time of year, you have to look at a couple of things.

"You have to look at the players for the 2009 season, maybe the 2010 season, along with blocking a player going to a team that may be in your division or may be in your league where you don't want to see them end up. So there are a number of things that go into the whole waiver process.

"They are not supposed to be talked about," Williams said. "And it's a shame, whether it be executives at other Major League clubs or in the Commissioner's Office or whomever. It's a shame that these things are talked about because we have talked about it on an ongoing basis at every general managers' meeting, that you are not supposed to release these names."

Releasing the names is not fair to the players, not fair to the team and not fair to the fans because they don't get a full view of how the waiver process works, according to Williams. Although Williams would not talk about Rios specifically, the Toronto outfielder previously has been on the White Sox radar.

Rios could step in to a starting outfield spot for 2010, assuming the mutual option held by Jermaine Dye and the White Sox is not picked up. He provides speed, power, a good bat and a strong outfield arm.

But the question remains as to where Rios would fit in as part of the current White Sox playoff push. There is no short-center fielder allowed in the Majors, and the White Sox have three solid outfielders in place. Rios also is playing in the second year of a seven-year, $69.5 million deal, plus a 2015 club option, which would be a sizable sum to take on even with salaries such as Dye, Jim Thome, Octavio Dotel and Jose Contreras coming off of the 2010 payroll.

Those questions just might be answered Tuesday, which would be the deadline for this particular waiver claim. As for any sort of change to the pitching staff, such as the possibility of bringing in John Smoltz, Williams didn't sound inclined to make a move with Jake Peavy's return targeted for the end of August.

"I'm very reluctant to make any changes, other than what we have already in house," Williams said.