Kaino, 36, lifted the World Cup with New Zealand in 2011 and 2015 but finished playing for the All Blacks two years later when he moved to play in the Top 14.
"Fingers crossed we get a lot more guys on the international level and the next couple of days hopefully we get more in Les Bleus," he said following the 24-18 victory over Clermont on Saturday.
"The next step for us is to develop and to challenge the rest of our group to get honours and get to as many guys in international teams, whether it's France, South Africa or other teams," the 81-time All Black added.
The influential pair of fleet-footed back Cheslin Kolbe and powerful but uncapped loose forward Rynhardt Elstadt are two in with a shout of featuring for the Springboks at the tournament in Japan after impressive club seasons.
"They have got a huge chance of making the South Africa squad. Rynhardt is just a machine, he's been great for us, he can run all day," Kaino said, who faced the Boks in 15 Tests for the All Blacks.
"I've been in a proud position to sit back and to watch them perform and to also see Kolbe get a call-up to the Springboks squad," he added in reference to Kolbe's Springbok debut in September 2018 after scoring 10 tries in his first season with Toulouse.
Elstadt, 29, played for the Springboks U20s side in 2009 and worked under South Africa head coach Rassie Erasmus at the Stormers and said he had discussed a potential call-up earlier in the campaign.
"They did talk to me about playing for the Springboks but nothing official or anything. The focus was just to finish the Top 14," he told AFP earlier in the week.
"There was nothing said like 'after the season I could play for them' nothing at all. For Cheslin and myself we just gave our everything to the Top 14," he added.
France head coach Jacques Brunel announces his 31-man squad for the World Cup on Tuesday.
Toulouse's Thomas Ramos who played at flyhalf in the final despite featuring mainly at fullback for France and his club this season, said he would happily wear the French No 10 shirt.
"I will look for my name, whatever the position. After winning this title playing at a World Cup would be massive, so I'll just look for my name," the four-time international said.
"If they ask me why not? I've still got some inconsistencies in the position. To play there I have to play more games there back-to-back, but the season is over now! I feel ready to play," he added.
Veteran Kaino's contract at Stade Ernest-Wallon comes to an end next June when he is expected to retire but is open to staying in France in a coaching role.
"I'd love to stay in France for as long as I can. When you're enjoying it so much you never you never put an end date to anything and you never say never. I'm getting a bit long in the tooth and a little bit older but I'm enjoying it so much that I'm open to anything," he added.