The Highlanders midfielder was left out of the All Blacks squad for the British and Irish Lions series, with Toulon swooping in for his services with the bid.
Sources told Midi Olympique on Friday (NZ time) the club was optimistic of securing the 25-year-old's signature.
Fekitoa is off contract at the end of the season, but said in April he was in no rush to make a decision on his future.
"I don't have a timeframe," Fekitoa said. "I let my management team do all the talking behind the scenes. For me, it's about getting my game right and enjoying my rugby."
Midi Olympique reported in November Fekitoa and Israel Dagg met up with the Toulon owner at a hotel during the All Blacks' end of year tour, with Dagg receiving an offer for his services.
Dagg ended up re-signing with New Zealand Rugby in February.
Toulon currently have former All Blacks midfielder Ma'a Nonu on their books.
Photo: Getty Images (Highlanders midfielder Malakai Fekitoa could be off to play rugby in France if reports are to be believed).