Dr Helmut Marko says Pirelli "has promised" to change its tyre compounds in time for next month’s Bahrain grand prix.
Together with Mercedes, Red Bull has been pushing F1’s Italian supplier to change tack after claiming the 2013 tyres are penalising the best cars.
"There are definitely signs about a change of the compound," Mercedes’ Toto Wolff was quoted as saying by SID news agency.
"In all probability, either in Bahrain or maybe after," he added.
Officially, motor sport director Paul Hembery insists Pirelli would only change its tyres mid-season if all the teams make an "unanimous" request.
"That is definitely not the case," he said.
But Red Bull’s Marko said on Sunday: "We are having to tell our drivers to go through the fastest sections not as fast as they can, because it’s too high a load for the tyres.
"Of course we have had serious talks (with Pirelli)," he told German television Sky.
"I think Pirelli has realised (the situation) and we have been promised that other compounds will come to Bahrain at the latest," added Marko.