Both Isco and goalkeeper Keylor Navas have become "very angry" at their lack of game time and have already received offers to leave, according to Manuel Esteban of AS (h/t Calciomercato.com).
The Spain international is a target for both Serie A sides when the transfer window re-opens in January, per Calciomercato.com.
Isco has only made five La Liga starts this season, but he did endure a spell on the sidelines after undergoing surgery for appendicitis in September.
Solari replaced Julen Lopetegui as manager on a caretaker basis in October. He has yet to start Isco in the three games he has taken charge of against Melilla, Real Valladolid and Viktoria Plzen.
Los Blancos have won all three matches under Solari. Barring a poor result against Celta Vigo on Sunday, the club will appoint him on a permanent basis until the end of the season, according to Deportes Cope's Melchor Ruiz (h/t Sport's Ariadna Valls).
If Solari is handed the role, it could spell bad news for Isco. ESPN FC's Dermot Corrigan believes he will not be happy with a reduced role:
Real Madrid do not lack for attacking options, with Isco battling Marco Asensio, Dani Ceballos and Lucas Vazquez for a place in the team.
At his best, Isco is one of Europe's most exciting, creative attackers. He's a skilful player, capable of unlocking defences and scoring goals.
He's been at Real Madrid since 2013 and has won La Liga, the Copa del Rey and four UEFA Champions League titles with the club.
Yet he's also been linked with a move away from the club in the past. He fell out of favour under Zinedine Zidane last season and said on March, "In Madrid I don't have the confidence a player needs," per Marca.
It's unlikely Real Madrid would be willing to let Isco leave the club. However, if he remains on the sidelines, it may offer other clubs hope he can be lured away.