The 27-year-old is widely expected to be one of several stars to leave Stamford Bridge this summer following an unsuccessful loan at Aston Villa.
According to journalist Fabrice Hawkins, Villarreal are the latest in a long line of clubs to register an interest in Disasi.
Following the sale of Álex Baena to Atletico Madrid and the imminent departure of Thierno Barry to Everton, the Spanish club are looking to reinvest some of that money.
Chelsea are requesting a fee of £25 million for the unwanted defender, with Newcastle United and a host of Serie A sides also interested.