Twente chairman Joop Munsterman has met McClaren to show him around the club's Grolsch Veste stadium and is waiting for a response from the Englishman.
He said: "We want a coach who is accustomed to working with top players."
Munsterman admits most fans of the Enschede club are sceptical about a coach who failed to guide England through qualification for Euro 2008.
He added: "Ninety percent thinks: why McClaren?
"But believe me, if he becomes our coach we will have a coach who is accustomed to working with top players and he can recognise them."