The Fenerbahce forward has made it clear the playmaker remains a key figure for Oranje, insisting his teammate "personifies" Dutch football.
Sneijder has not featured for Holland since the 4-1 win over Hungary on Sept. 11 last year, with Kuyt and Kevin Strootman wearing the captain's armband during his absence.
Nevertheless, the Fenerbahce attacker has made it clear there is no doubt about Sneijder's position as first-choice skipper.
"Sneijder is our undisputed captain. I'm deputy skipper and Kevin Strootman is the third man in line," Kuyt told Goal.com. "Wesley has not been part of the team for a while, but he's back again now. Everybody can expect Wes to be wearing the armband in the months to come. The captain always plays, unless he's injured.
"He's a great player and personifies Dutch football. It's a shame that his time at Inter came to such an end, but he continues to be a fantastic player. We don't even have to discuss his football qualities. He's very valuable for the team both on and off the pitch. He's a real leader with a lot of experience, and has played at several major tournaments. He leads younger players the way and is very committed."
Sneijder has made 90 international appearances so far for Oranje, scoring 24 goals in the process.