"Russia has to make a request to wave her immunity," Brasseur said at an informal meeting with reporters in Strasbourg, adding that "immunity does not mean impunity."
Brasseur said that Russian authorities should proceed with their investigation.
"If she is sentenced and it is done accordingly to the rules, with all the proof, we have to take that into account," she said.
However, Savchenko is currently in pre-trial detention and has not yet been proven guilty, "so she must be allowed to attend our Assembly," the PACE head added.
Savchenko has been detained in Russia since mid-2014 over her suspected role in the killing of two Russian journalists who were covering the Ukrainian conflict.
In October, Savchenko was elected to the Ukrainian parliament for Yulia Tymoshenko’s Fatherland party, gaining parliamentary immunity. She has also been named as part of Ukraine's delegation to PACE.
