The team approached Bross the week after the All-Star Game, when the Marlins were playing the Rockies in Miami, and the agent said on Friday that talks were "preliminary."
"I'm not sure where it's going to go," Bross said.
Bross was in Cincinnati, where the Marlins are playing the Reds for three games, and was expected to have further discussions with Marlins general manager Michael Hill.
Bross did not go into parameters of the contract, but discussions are believed to revolve around a three-year deal. Per team policy, the Marlins do not comment on negotiations.
Currently in his second year of arbitration, Uggla is making $7.8 million, which is the highest contract for any Marlins player this season. If he remains unsigned, 2011 would be the final year he is arbitration-eligible before he would have the required MLB service time to pursue free agency.
The Marlins have plans to keep Uggla for at least three more seasons, meaning he would remain a fixture next to three-time All-Star Hanley Ramirez.
Uggla is in the midst of his best season, batting .284 with 26 home runs and 72 RBIs.
On July 31 at San Diego, he connected on his 144th home run with the Marlins, making him the club's all-time leader, as he surpassed Mike Lowell's 143.
Heading into the weekend series, Uggla has 147 career home runs. Twice he has been an All-Star -- 2006 and '08.
Uggla is in strong position to win his first Silver Slugger Award for a National League second baseman.
A Rule 5 Draft pick out of Arizona's system in 2005, Uggla is the only Marlins player to post three straight 30-homer seasons. He is on his way to making that string four in a row.
No second baseman has hit more home runs since 2006 than Uggla.
A subject of possible trade talks for more than a year, Uggla has entrenched himself with the Marlins, who regard him as a valuable leader and a building block player.
The Marlins currently have Ramirez (six years, $70 million) and Josh Johnson (four years, $39 million) locked up to multi-year contracts. If Uggla joins them, the club will have three centerpiece veterans under contract by the time they move into their new, retractable-roof stadium in 2012.
The Marlins also are exploring signing pitcher Ricky Nolasco to a multi-year contract. Like Uggla, Nolasco is in his second arbitration year.