Sources close to the Spanish club say Swansea have until 20 June to exercise their option to sign the Canadian-born Dutch international.
The Welsh outfit will have to pay at least €6million for the 25-year-old, who made 33 Premier League starts last season and scored twice in Swansea's Capital One Cup final win over Bradford City.
Both De Guzman and Swansea have been open in their hope that a permanent deal could be struck, while Villarreal appear keen to sell the midfielder despite recently returning to Spain's top flight.
Swansea are looking to retain De Guzman's services despite the recent speculation over the future of manager Michael Laudrup.
De Guzman's success at Swansea lead to his full international debut for the Netherlands last season, and he was in action for his country in their 2-0 win over China in Beijing on Tuesday.