Terms of the deal aren't known, but Mozeliak told ESPN 101 in St. Louis he expects an answer from Holliday's agent, Scott Boras, within 48 hours. Mozeliak told MLB.com he could hear something back by this weekend.
Boras couldn't be reached for comment.
"We did make an offer," Mozeliak said. "Obviously we would love to have him back."
Holliday, 30 in January, hit .353 with 13 homers and 55 RBIs over the final 63 games of the regular season after being traded to St. Louis from the Oakland A's.
"Obviously, his bat in our lineup changed it," Mozeliak said. "So when you consider that, we thought he was a key component."
If Holliday signs soon, the market for the other prized free-agent left fielder, Jason Bay, will no doubt heat up, with several teams interested in his services.
Boras has compared Holliday to one of his other clients, Mark Teixeira, who signed an eight-year, $180 million deal with the Yankees last offseason. But the Cards reportedly rejected that comparison.
If the Cardinals can't get Holliday back, Mark DeRosa has been seen as a potential Plan B. But Mozeliak told the St. Louis Post-Dispatch his club has not extended multiyear offers to anyone beyond Holliday.