Isco has only made fleeting appearances totalling 88 minutes since Solari replaced Julen Lopetegui as Real boss seven matches ago.
Marca reports on Thursday ahead of the game that Isco will be handed the armband for the last-32 match.
They add that Vinicius will also play, alongside Marco Asensio.
Isco's fitness has come under scrutiny amid his first-team omission.
On Sunday, after he only played 10 minutes against Valencia that weekend, he posted a picture of himself shirtless with the question 'am I fat?'
Despite his minimal involvement, Isco's team-mate Dani Carvajal has come to his defence.
The full back told realmadrid.com: "He is the most loved in the dressing room, like Marcos Llorente."
Isco has also been linked with a move to Serie A giants Juventus but reports in Spain suggested the move could be curtailed by his whopping £623m release clause.
Real lead Melilla 4-0 from the first-leg of the cup tie.