The Ukrainian enjoyed a successful loan spell with Hertha last season, his goals helping them secure a fourth-placed finish in the Bundesliga.
He has since returned to Anfield, but his chances of regular first-team football under Rafael Benitez look bleak.
"Yes, I have contact with Andriy, just spoken to him on the telephone," Favre said in the Bild newspaper. "The contact was never broken off. He played excellently for us."
A transfer fee could prove a stumbling block, though.
Hertha general manager Michael Preetz added: "We would like to have Voronin - if it was financially doable."