The Spaniard has struggled to stake a regular claim for a spot in Madrid's starting XI under Santiago Solari, with Goal revealing that the situation is a 'ticking timebomb' that would likely result in the midfielder leaving the club.
Barca have been mentioned as one of the teams that may hold an interest in signing Isco, with former forward Rivaldo having been one to publicly state that he would like to see the 26-year-old move to Camp Nou.
Indeed, he's only made five league starts in 2018-19 as Madrid prepare to face Barca in Wednesday's Clasico clash in the Copa del Rey semi-final.
Isco's lack of regular football has frequently seen him linked with a Madrid exit although he did not leave for a European rival in the January transfer window, with his contract running until 2022 and the club seemingly in no rush to sell.
And when asked whether Barca would contemplate signing Isco, Bartomeu insisted there is no block on bringing players in from their rivals and that he would facilitate such a deal, should the head coach ask for it.
"If our coaches asked us for a player and they want to leave Madrid, of course we would sign them," he told El Partidazo de COPE .
"But it has not happened since I've been here.
"There are no non-aggression pacts. Each one tries to make their team more competitive.
"Isco? For the sake of Real Madrid I would speak with the president of Real Madrid [Florentino Perez]."
Barca are currently enjoying supremacy over their rivals in league terms, with the Catalans eight points clear of Solari's side at the top of the table.
Madrid, who are third in the standings, have enjoyed something of a renaissance in recent times, though, winning their last four league matches in a row to pull themselves back into contention.