Mercedes' Niki Lauda, who like Red Bull has been complaining the loudest about the fragile tyres and their impact on F1 this year, said in China that Pirelli has agreed to supply more durable compounds for Barcelona and beyond.
Hembery, Pirelli's F1 boss, acknowledged the legendary triple world champion's words, but insists the Italian marque "needs these four races" at the start of the calendar to fully unfold before decisions are made.
"If we do make changes, we'll announce it after Bahrain and in time for Barcelona," the Briton promised.
It is believed the straw that broke the camel's back regarding Pirelli's likely change of tack has been an argument based also on safety.
Former grand prix driver Olivier Panis explained: "Pirelli is not 100 per cent to blame.
"I think we (F1) asked them to do things for the show, and they followed the specifications.
"So I don't want to throw stones and criticise, but it has gone too far," said the Frenchman, who now travels to races as French driver Charles Pic's advisor.
"Now it is a safety problem. We saw (Jenson) Button's tyre burst because of a flat spot (in China), but it's important not to have failures like this when you are going 300.
"That's what scares me; the safety. There is degradation and yes it's the same for everyone but we have to be careful it does not go too far," Panis told RMC Sport.
Another possible change for Barcelona is an extra set of tyres for teams to use on Fridays, encouraging more action rather than the new common practice of saving tyres in the pits.
Hembery said Pirelli would be "happy to promote" that idea, which was proposed by Force India deputy principal Bob Fernley.
The concept would be that teams qualify for the extra, more durable tyres if they pledge to fit them to a car piloted by a non-race driver.
But Hembery said all the teams are yet to agree, mainly because while the small teams would be happy to run a young or reserve driver, the same is not true of the top teams.