Peavy, who was teammates with Gonzalez in San Diego, gave Williams information about the slugger's character as well as his ability during their conversations.
"Obviously, Kenny asked me at one point [last winter] what kind of a guy Gonzalez is," Peavy said. "I went into full recruiting mode. Let me tell you something. This guy is as good a player as there is in the big leagues. I know a lot of people don't get to see him because he plays in San Diego. Adrian Gonzalez! It doesn't get a lot better than that.
"You put [Albert] Pujols and maybe a few guys above him, but he hits 40 home runs where he doesn't get much protection in a huge ballpark [Petco Park] in a division where pitching is prominent. I said [to Williams] listen, if you put this guy in the mix on this team, a left-handed bat in the middle of the lineup, a guy that could spell Paulie [Konerko] at first and is a Gold Glover. There is not much bad about the guy.
"I told Kenny absolutely if you put this guy on your club he's a great person as well."
The Padres have been approached by numerous teams in the offseason about the availability of Gonzalez. The smart money has been on the Boston Red Sox as the ultimate front-runner if a trade is ever worked out.
The Padres have hesitated to trade Gonzalez up to this point because he is a San Diego native and one of the only reasons to buy tickets to watch a young and upcoming Padres team.
Gonzalez batted .277 with 40 home runs and 99 runs batted in last season. Gonzalez, 27, is a career .285 hitter and has averaged 32 home runs and 100 RBIs in four seasons with the Padres.
With new ownership, the Padres are trying to show as much fiscal restraint as possible because they came in under capitalized. The San Diego market also is difficult to project as far as corporate sponsorships and tickets sales because the 40-man roster is in transition.
The White Sox have been looking for for production from the left side since they decided not to re-sign Jim Thome. The White Sox missed out on Johnny Damon, whom they offered a one-year, $6 million deal before he signed with Detroit for $8 million.
The Gonzalez story was first reported by CBS Sportsline.
Bruce Levine covers baseball for ESPNChicago.com.