That time is over. The White Sox traded for pitcher Jeff Samardzija and agreed to terms with closer David Robertson on Monday, on the heels of signing free-agent first baseman Adam LaRoche and left-handed reliever Zach Duke.
The White Sox are playing to win, and win now. That means Ramirez is no longer available, no matter how much interest other teams might have.
"You're talking about a premium player at a premium position who is signed to a reasonable contract," White Sox General Manager Rick Hahn said Tuesday.
Ramirez, 33, made his first All-Star team last season, when he batted .273 with 15 home runs and 21 stolen bases. He is signed for $10 million next year, with a $10-million club option for 2016.
The Dodgers and White Sox talked some time ago about Ramirez for Matt Kemp deal, according to a person familiar with the discussions, but the two sides could not agree on the financial structure. Kemp has $107 million left on his contract.
Jimmy Rollins of the Philadelphia Phillies would be a likely target if the Dodgers decide to trade for a shortstop. Rollins has the right to veto any trade, and the lower-level prospects the Dodgers would probably offer might not be enough to entice the Phillies to part with a player so closely identified with their glory days.
Samardzija, acquired for four prospects in the Oakland Athletics' latest roster revamp, is eligible for free agency after next season.
"We're going to make every effort in the coming weeks and months to try to make this a long-term relationship," Hahn said.
"You're not going to have a break when you come through Chicago and face this rotation," Hahn said.
The White Sox also have left-hander Carlos Rodon, the third overall pick in last June's draft. Rodon could be ready this season.
Samardzija played football at Notre Dame, to which Hahn alluded as he lauded Samardzija's competitiveness.
"As a Michigan grad," Hahn said, "I saw that first-hand."