In the aftermath of Honda's withdrawal from F1 for financial reasons last December and Brawn's emergence from the ashes, Button accepted a pay cut of £5m - taking his salary to £3m - for the sake of his new team.
With Button having claimed the drivers' title with a superb fifth place in difficult circumstances at Interlagos, helping Brawn to the constructors' title in their maiden F1 season in the process, it is believed that Button could be looking to restore his salary to its previous amount.
Fry jokingly admitted that Button's success would probably "make him more expensive" but he remains confident that the 29-year-old wishes to remain with the team.
"We've been together a long time, its six or seven years now," said Fry. "We've been through the hard times together and now we're successful. We've got to do a bit of negotiation.
"There are a number of people who have signed with the team, or are effectively competing with each other to be part of the team so I've no worries over that."
Brawn's success this weekend is a far cry from the start of December 2008 when Honda pulled the plug on their F1 operation because of the pressures of the global financial crisis, leaving team boss Ross Brawn and Fry to pick up the pieces.
"At the beginning of this year we were close to the edge on several occasions, and a couple of times we did think that all was lost," said Fry.
"We had to take it one step at a time because it was easy to get overwhelmed by a situation.
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"We just took every race one at a time and did the best we could, and we have become world champions."
Cost-saving measures saw Brawn forced to make 270 staff redundant in March 2009 and Fry was keen to pay tribute to their part in the team's subsequent success.
"If you don't make those decisions then everyone's out of a job, and that's no consolation for the people who unfortunately had to leave the team," said Fry.
"I hope they feel just a little bit a part of this. In many cases there are people who had worked for the team for six or seven years, and who had put in a lot of effort into it."
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