Pirelli has insisted it is willing to stay on in the sport once its current contract expires at the end of the 2013 season, although the Italian firm has made it clear it would only extend its deal as long as it made sense financially.
AUTOSPORT analysis: F1's brewing tyre dilemma
As talks continue between Pirelli and the teams, Hembery said that delays are not beneficial for the company.
"The more time it passes, the more difficult it becomes," Hembery told AUTOSPORT.
"We are in the automotive business and I think anyone reading the newspapers will see that Europe is performing particularly badly in our sector.
"We are not immune to that, and the more time that passes the more questions that get asked at board level.
"We have to keep asking and justifying our involvement in this sport. We are willing to go forward in the sport, but I always said that it won't be at any cost because that simply can't happen.
"We put a value on the sport and we can't go beyond that because we have an obligation to our investors."
He added: "The more time that passes... maybe big companies change their minds. I hope that doesn't happen.
"It's certainly not the discussion at the moment, but we do look at the numbers and it's obviously bleaker every day at the moment.
"You can't divide what's going on in the business community with what you are trying to do in terms of branding and promotion."
Hembery suggested most F1 teams have already agreed on the terms for a new deal, but admitted there was still points to sort out with others.
"We've got a good number of teams wanting to carry on. There's a couple of discussion points with a few teams, but that's normal in this sort of process," he said.
"We just need to find a rapid agreement that meet everyone's satisfaction."
When asked what those discussions points were, he said: "Primarily commercial."