According to Midi Olympique, Kaino was in discussions with the Top 14 side during the All Blacks' recent Northern tour.
His current contract with New Zealand Rugby goes through to the end of the 2018 season.
Kaino had to return home during the French leg of the tour due to a posterior cruciate ligament injury suffered in the Barbarians match.
The 34-year-old, 81-test veteran, was fighting to resurrect his international career after being bumped down the loose forwards pecking order.
"It's not the end of his test career at this point. He's got to go home and do what everyone else does and play well in the Super season and then we'll start again," All Blacks coach Steve Hansen said at the time.
According to Midi Olympique Kaino would replace Springbok Duane Vermeulen, whose contract expires next June.
Former All Blacks Ma'a Nonu, Malakai Fekitoa, Luke McAlister and Alby Mathewson all currently play for Toulon.
Kaino has previously played in Japan for three seasons, joining Toyota Verblitz after the 2011 Rugby World Cup.