Okdiario says an agent for the former Barcelona ace was in Madrid on Friday to offer the Spain international to the European champions.
The reponse was positive. Real chiefs considered the proposal from the agent and did not rule anything out. However, any final decision will be left to the new coach. Zinedine Zidane, before his resignation, had discussed moving for Thiago with club directors.
A return to Barca is also being considered, with technical manager Guillermo Amor opening the door publicly last week.
Okdiario's chief pundit Eduardo Inda has also revealed that "Barca have made direct contact and trying everything to re-sign Thiago".