The 50-year-old is keen to sample life on the international stage, with his contract due to expire at the end of the season
The former PSV boss took charge of the Arnhem side at the start of the 2012-13 campaign, and has guided them to fifth place in the Eredivisie table halfway through the season.
"I'd like to become a national team coach. You have to experience all kinds of things in your coaching career," Rutten told Omroep Gelderland.
"Ideally, I'd take charge of a foreign team. You're dealing with different conditions then. I am a very curious guy.
"Wherever I go, I want a job with perspective and where I can build on something."
Rutten's contract with Vitesse is due to expire at the end of this season.