Real Madrid president Florentino Perez is reportedly considering an approach for Valencia boss Marcelino.
Solari's reign started with a 4-0 win over Melilla in the Copa del Rey on Wednesday night, but the 42-year-old is reportedly not under consideration to become the permanent manager.
Tottenham Hotspur's Mauricio Pochettino has been strongly linked with the position, but according to Don Balon, Marcelino is also in the frame, with Madrid president Perez a huge admirer of the Spaniard.
Marcelino managed Villarreal between 2013 and 2016 before taking the position with Valencia, and led Los Che to a fourth-place finish in La Liga last term.
The 53-year-old's current deal at the Mestalla will expire at the end of this season.