Off contract from Villarreal, Albiol announced upon his departure that he wanted to play on this season.
TMW says Albiol is now in advanced talks with Serie A new-boys Pisa.
Now 39, Albiol is close to signing a one-year contract worth €500,000, plus an appearance bonus.
There is great optimism about the Serie A return of the Spanish defender, who previously played in Italy, at Napoli, for six seasons from 2013 to 2019, making 236 appearances and scoring six goals.
He recently stated: "The idea is to continue playing. The dream is to do it in Italy. I've never thought about retiring. I'm still competitive. My contract with Villarreal has just expired, and now I'm waiting.
"My family and I have a dream: to end our career in Italy. We had a great time in Naples; it's a country very similar to Spain. Our door is always open to Italy."