Team executives and Lozano emerged from the meeting, which lasted about one hour, 15 minutes, with neither side commenting.
"Can't," Marlins president David Samson said when asked if he could comment. Samson earlier had told reporters, "We will definitely have stuff for you this afternoon."
The sides planned to resume talks Wednesday morning.
The dollar amount is believed to be more than $200 million for the nine-time All-Star and three-time MVP. The Cardinals also made a 10-year offer to their longtime first baseman on Tuesday, reported by the St. Louis Post-Dispatch as having the potential to reach $220 million. USA Today's Bob Nightengale reported Tuesday night that a mystery team has also offered Pujols a 10-year contract. Reports later in the night indicated that the Angels were the third team to present a 10-year deal.
It was not known whether the quiet exit from the meeting was an indicator that Lozano and Pujols planned to speak with the Cardinals before acting further on the Marlins' offer.
The two sides were negotiating a no-trade clause for the first five years, FoxSports.com reported, to cover the time until Pujols would regain 10-and-5 status, by which players can veto trades.
The Marlins were pushing for a resolution Tuesday night because they want to know if they need to move in another direction. A fallback option could be Prince Fielder. Miami officials remained holed up in their suite late into the night Tuesday discussing their offer to Pujols and weighing their options.
For weeks the Marlins have been in discussions with Pujols' agent, and the team would like to bring some closure to the process. In addition to Samson, owner Jeffrey Loria, president of baseball operations Larry Beinfest and general manager Michael Hill attended Tuesday's meeting. Buster Olney of ESPN and FOXSports.com's Ken Rosenthal reported Tuesday evening that the Marlins' front-office contingent met with MLB executive Dan Halem about matters concerning a possible Pujols contract.
The Marlins turned their attention to Pujols on Monday after they reached agreement on a six-year contract with All-Star shortstop Jose Reyes. An announcement on Reyes is expected on Wednesday afternoon.
The Marlins met with Lozano on Monday, a few hours before they introduced Heath Bell as their new closer. They met with Lozano again later in the day. Pujols visited Miami a few weeks ago, taking a tour of the team's new retractable-roof ballpark.
Marlins manager Ozzie Guillen is excited about the aggressiveness of the team in its quest to land as many impact players as possible. Unlike in years past, the Marlins are willing to make sizable offers to impact players in hopes of building an immediate contender.
"They're working very hard, and they are showing people they're for real," Guillen said. "This is not for marketing. They're for real. As a manager, you appreciate that."