Vizquel, who will turn 42 on April 24, hit .222 in 92 games last season with the Giants.
Vizquel is a career .273 hitter who has spent the last four seasons in San Francisco. He started his Major League career with the Mariners in 1989 and has won 11 Gold Glove Awards, the last in 2006.
The Padres currently plan on using Luis Rodriguez at shortstop, but general manager Kevin Towers has said he would like to add middle-infield depth, possibly in a trade.
There have been rumors that if the Padres pull off a trade of pitcher Jake Peavy to the Cubs, they would receive shortstop Ronny Cedeno in return.
No Vizquel deal is expected soon, as the Padres have focused their sole attention on getting a trade done for Peavy at the Winter Meetings, which end Thursday.
Corey Brock is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.