The Bears are in the midst of a widespread recruiting raid under master coach Mal Meninga ahead of next year's highly-anticipated entry into the NRL.
Meninga has already poached two Sharks players - Tongan international Siosifa Talakai and Kiwi centre Chris Vea'ila.
And it seems like the Bears have their eyes on a few more Sharks, with co-captain Cameron McInnes and fullback Will Kennedy reportedly on their hit list.
McInnes, 32, is in the latter stages of his recovery from an ACL tear and would make an ideal inaugural captain at the Bears.
"He's a terrific man, terrific leader," Fitzgibbon said ahead of his team's clash with the Sydney Roosters in Perth on Saturday.
"He's coming back soon from an ACL injury, and just such a fantastic guy and leader that it'd be an asset for any club that he's at.
"He's definitely an asset for the Sharks, and it won't be without a fight."
Kennedy is one of 13 Sharks off contract at year's end, and the 28-year-old is open to a move away from Cronulla.
"It won't be without a fight," Fitzgibbon re-iterated when asked about the Bears potentially trying to sign Kennedy.
Fitzgibbon had mixed feelings about losing Talakai and Vea'ila.
"Look it hurts, because we would have liked to have kept those players," he said.
"But we're also happy for them and proud as a club that if we've had a player in our service that's got a better opportunity for him and his family, then we're doing our jobs as Sharks to offer that to the players."
The Sharks finished fifth on the home-and-away ladder last year, fourth in 2024, sixth in 2023 and second in 2022.
They currently sit seventh with a 3-2 record, and Fitzgibbon would love to keep the bulk of the squad together for at least another year.
"We've been really stable in our roster for a number of years now," he said.
"And what we've actively developed behind the players that are playing in the NRL team, we've got a crop of players that are ready to come into positions over, if not in the next 12 months, the year after.
"So we've positioned ourselves with some ready-made replacements that we value and think are going to be good players in the future."
Sharks centre Jesse Ramien will be sidelined for a month due to a knee injury.
The Roosters enter Saturday's double header in Perth, which also feature the Rabbitohs up against Canberra, with a 2-2 record.