Assistant general manager David Forst, who arrived from Oakland late Monday afternoon and will hold down the fort until GM Billy Beane shows up on Wednesday, would not say if there is an actual offer on the table.
But it could be just a matter of days before Thomas' replacement is in place.
"I think we will know more by the end of the week," Forst said.
As of Monday night, no face-to-face discussions with Piazza or his agent -- Dan Lozano -- were scheduled for the remainder of these meetings. However, the two sides have been in almost daily phone contact for several weeks.
"We'll have more conversations while we are here," Forst said.
Piazza, who has spent his entire 15-year Major League career in the National League, has at least one other team seeking his services. The American League West rival Texas Rangers also are in pursuit.
Forst said he wasn't surprised to hear that the Rangers entered the picture.
"They need to replace some bats," he said.
In the big picture, the Athletics might have more to offer.
They are the defending division champions, contend for the division title practically every season, play in much cooler weather during the summer and are located in California.
"Coming here, he would have a chance to get everyday at-bats as the DH and have a chance to be on a team we think will again compete for the American League West," Forst said. "And we have a nice track record the past several years of bringing guys in and providing a good atmosphere for them to succeed."
He listed Thomas, John Jaha and Matt Stairs as examples.
The Athletics hit the jackpot last season by signing Thomas, who was coming off a couple of injury-plagued seasons with the Chicago White Sox. His health was fine, and his hitting brought back memories of a young Big Hurt as he belted 39 home runs and drove in 114 runs.
Thomas accepted a lucrative contract offer from the Toronto Blue Jays, leaving the Athletics with a gaping hole in the lineup and hoping that their rich AL history lands them another future Hall of Fame player.
Though Piazza is a 12-time All-Star catcher, the Athletics want him for his bat.
"It depends on the makeup of the team, but coming in, he would be the third catcher if he were here," Forst said. "So, whether there are enough innings for enough games for a third catcher to get, I don't know. Obviously, we are thinking about him as the DH."
Jason Kendall will return as the regular catcher, and Adam Melhuse, eligible for salary arbitration, figures to handle the bulk of the backup duties.
While the A's wait for what they hope is a happy ending in their pursuit of Piazza, they also are preparing to make a move that could help absorb the loss of starting pitcher Barry Zito.
Forst confirmed that the team is very interested in signing left-handed reliever Alan Embree, which would open the door for left-hander Joe Kennedy to move into Zito's spot in the rotation.
Embree, 36, has pitched for eight organizations during his 13-year career, and this past season was one of his best. He had a 4-3 record and 3.27 ERA in 73 relief appearances for the San Diego Padres.
"We have talked to Alan's representative," Forst said. "[Embree] is someone we're definitely interested in. He could be a good fit here. Putting him out there would free up some options, as far as the rotation is concerned. We have a lot of good internal options."
The fact that Beane won't even arrive until the four-day meetings are three days old suggests that the A's are not going to be one of the busiest teams during these sessions.
"We've got a good foundation in place," Beane told the San Jose Mercury News on the eve of the meetings. "We like our team, so there's no real sense of urgency on our end. Most of our team is already in place."
Adding Piazza and Embree would practically put a bow on the total package.