The former Forest Green Rovers striker, 26, has netted 28 times in all competitions for Rovers this season.
His goals have helped the club up to fourth ahead of the season's final day.
"We have an understanding that, if he comes to us and he's got an offer, we'll have a chance to match that offer," Hamer told BBC Radio Bristol.
"If that offer, unfortunately, is so incredibly good for Matty but not very good for Bristol Rovers Football Club, we'd probably have to decline matching it.
"Because, if you're so lopsided, it can de-stabalise the rest of the squad because somebody's on an amount of money.
"He's got an agent that's doing the best job he can for him. But that's not to say we're going to give that one up without fighting."
Hamer also revealed the club would discuss a new contract with manager Darrell Clarke at the end of the season, with Rovers guaranteed at least a play-off spot, lying one point off the top three ahead of Saturday's visit of relegated Dagenham & Redbridge.
"At the moment, we're not distracting him (Clarke) from the job in hand," Hamer said.
"As soon as that's over, we'll sit down and have a chat with him. There's no reason why we can't come up with something that's going to please him and please us.
"The job he has done is remarkable. Having got to know him, I think he could go a long way in this game. He's tactically very aware.
"It would be nice to think he can get to where Eddie Howe is at Bournemouth. There is no reasons why he can't.
"I'd like to think he'll join us on an exciting journey that we've got going forward, but who knows?"
Clarke says Rovers' rivals have "everything to lose" on Saturday and his side would be "very unfortunate" not to go up if they finish on 85 points.
Bristol Rovers will have the chance to match offers made by other clubs for League Two's top scorer Matty Taylor this summer, says chairman Steve Hamer.