Red Bull could take part in a tyre test using a two-year-old car, but don't expect their drivers to be wearing "nondescript helmets".
Mercedes and Pirelli were both reprimanded by the FIA's International Tribunal in June while the former were also banned from the Young Driver Test at Silverstone after they conducted a private tyre test in May.
Ferrari also took part in a tyre test with Pirelli at an earlier stage, but while they used a 2011 car with their Corse Clienti division doing the test, Mercedes ran their 2013-spec car.
Another big point of contention was that Mercedes ran their current race drivers with Nico Rosberg and Lewis Hamilton wearing unmarked plain black helmets during the test to avoid being recognised.
The FIA, though, has since given Pirelli permission to use any car for testing of its 2014 tyres, but it needs to be communicated to all teams.
Although no one has taken the Italian manufacturer up on it, Red Bull are now considering doing a test with their 2011 challenger.
Team principal Christian Horner told Press Association Sport: "We will see. It is something we have to discuss with Pirelli."
As for the importance of the test to Pirelli, he added: "That is for them to judge, what they need and what they require from testing.
"Whatever happens it has to be done transparently. We don't want people sneaking off behind closed doors - and wearing nondescript helmets."
The FIA has changed its tune since the testing scandal and are now trying to help Pirelli, but the company's motorsport director Paul Hembrey believes a lot more needs to be done.
"The FIA, on their part, have said they will open the door on it (testing), which is the good step forward," said Hembery, speaking to Press Association Sport.
"Now we need to sit down with the FIA, (president) Jean Todt and (race director) Charlie Whiting, and define what we really want.
"Then we'll go to the team principals and say 'Look, this is what needs to happen going forward'.
"That's irrespective of Pirelli. Anyone coming into the sport would need to do this."