That means when Chicago's exclusive five-day exclusive negotiating window closes at mindnight on Monday, both players would be open to negotiate free-agent deals with all teams.
Officially, the White Sox gave no indications on what move they would make and no announcement was forthcoming Monday night to indicate what decision they made.
By making a qualifying offer, the White Sox would have been committed to either player at $14.1 million (the average of the 125 highest contracts) for the 2014 season. If a player was extended a qualifying offer and didn't accept, that player's team would be compensated with a draft pick when he signed with another club.
After signing international free agent Jose Abreu last month, the White Sox are covered at first-base. Adam Dunn has one more year on his contract which would mean designated hitter spot is covered as well.
The White Sox still have not ruled out re-signing Konerko and plan to meet with him face-to-face this month to talk about the future. But the $14.1 million price tag was much more than they are willing to pay to a player who has never made that much in a single season. Konerko made $13.5 million in 2013, but $7 million of that was deferred.
With Floyd coming off Tommy John surgery and unable to start the 2014 season on time, he was not valued at upward of $14 million either. The White Sox picked up Floyd's option at $9.5 million in 2013.