Arsenal reportedly offered Real Madrid £40m for Isco in the summer.
The Spaniard is enduring a difficult spell in the Spanish capital, making just three La Liga appearances all season as he struggles with injury.
It does not appear as though the attacking midfielder is a key part of Los Blancos' future plans, and they are willing to part with the former Malaga man.
However, in the absence of a bid from Pep Guardiola's Manchester City, who had previously shown interest, Unai Emery and Arsenal offered £40m, according to reports in Spain.
The Gunners' bid was knocked back, and they instead landed Dani Ceballos on loan.
AC Milan are thought to have taken an interest ahead of the next transfer window, but they would struggle to offer a larger sum than Arsenal's rejected bid.
