The Ukrainian reportedly met with club officials, including general manager Dieter Hoeness and head of player licence Michael Preetz, on Sunday to discuss the possibility of him staying at the Olympiastadion beyond the end of the campaign.
"Yes, we have spoken for the first time," Voronin told the Bildnewspaper.
"It was a good talk. I think we are on a positive path," his agent Andrey Golowasch added.
Hoeness admits Hertha would like to keep hold of the forward.
"There is a willingness on both sides to continue further," he said.
"We value Andriy's performances very much - his goals, presence and experience.
"He also says Hertha are his top priority because he feels very happy with us and in Berlin. Now we have to look for solutions together."