Team officials met with the pitcher and his agent, Scott Boras, in Southern California on Monday.
The meeting -- which, according to The Seattle Times was more of a "get-acquainted session" than an open negotiation -- was attended by Seattle general manager Bill Bavasi and manager Mike Hargrove.
Zito -- considered the prized arm in this free-agent class -- met with the Mets on Tuesday in Southern California as well.
According to The Newark Star-Ledger, those talks were "productive and encouraging."
According to reports, Zito might command a contract similar to the five-year, $73 million deal Roy Oswalt received from the Astros. But Zito might get more.
The Rangers have reportedly offered a contract in excess of $100 million, though it's believed to be closer to five years and $75 million, according to the Star-Ledger.
Zito has also met with the Giants, in addition to the Mariners, Mets and Rangers.
The Mariners, who entered the offseason looking for in upwards of three pitchers for their rotation, have traded for left-hander Horacio Ramirez and signed free-agent right-hander Miguel Batista in recent weeks.
Bavasi was asked Monday if Seattle was done looking for upgrades to its rotation.
"I'd like to say for the peace of mind for all the starting pitchers that we're done, but that's not the way the real world works," he said.
The Mariners would likely have to extend their projected payroll for 2007 to sign Zito, though it might well be worth it if for no other reason than to keep him from pitching against Seattle.
Zito, who has a career record of 102-63 with a 3.55 ERA, is 12-2 with a 3.62 ERA in 23 career starts against the Mariners.
Corey Brock is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.