Rasul who has been in hospital in Sulaimani for several days is believed to be flown by a special plane to Turkey and from there to Berlin.
Dr. Dara Rasheed, Rasul's physician told Rudaw that the PUK leader's health has improved and he has begun eating and is able to speak.
"But, he is still under intensive care," he said.
After his health deteriorated on Saturday, Rasul was rushed to the hospital in Sulaimani where he underwent an operation.
The 64-year old Kurdish leader became the party's acting head after the death of PUK founder Jalal Talabani on October 3.
A day before his illness, Rasul was last seen attending a memorial held for Talabani, the party's deceased leader in Sulaimani on Friday.
He was Vice President of the Kurdistan Region until late October.
