Russian media outlet R-Sport reported that Voynov had received an offer from Traktor Chelyabinsk of the KHL, but that he's poised to return to the Kings.
Voynov's Russian-based agent, Alexander Tyzhnykh, informed R-Sport of Traktor's offer, but also revealed a deal with the Kings was near.
"We haven't given them an answer yet," he said. "But I won't hide it, Slava is leaning toward Los Angeles. After all, he's been in the Kings system for five years and everything in the organization suits him."
One separate source told TFP on Saturday that a long-term contract between the Kings and Voynov is in the process of being completed. The Kings did not immediately respond when contacted regarding the matter.
It has been widely reported that Voynov could earn at least $4 million, per season, on a new deal.
In all 48 games with the Kings this season, Voynov registered six goals and 19 assists for 25 points.