Jarrett Bousquet spoke to TSN Radio on Thursday after it was announced that Weber and the Flyers agreed to the offer sheet. The contract reportedly is for 14 years, $110 million.
Bousquet compared the chance for hard feelings to Weber's arbitration hearing with the Predators last offseason. He was awarded a $7.5 million contract after the team offered less.
"I think it would be very much the same case that if they were to match ... as soon as you hit the ice these guys are after one thing, and that's winning hockey games," Bousquet said.
"I don't foresee there being a problem in that regard."
Nashville general manager David Poile had said the team intended to match any offer Weber might receive, but in a statement Thursday said it "will take the appropriate time to review and evaluate it and all of its ramifications in order to make the best decision for the Predators in both the short- and long-term."
The Predators have seven days to match the offer. They could receive up to four first-round picks as compensation if they do not.
Bousquet said Weber would not have entered the agreement with the Flyers if he wasn't planning to play in Philadelphia.
"I don't think you sign an offer sheet unless you're pointing in that one direction ...," Bousquet said. "It's really up to [Nashville]. He'd like to play with the Philadelphia Flyers because I think we all feel that he's just another piece in the puzzle to take them to the next level and he doesn't want to go through a rebuilding process again."
Weber's defense partner, fellow all-star Ryan Suter, signed a 13-year, $98 million contract with the Minnesota Wild on July 4.