The 20-year-old Spanish under-21 international has attracted attention from a number of top European clubs, but Chelsea are keen to strike first before Malaga renew the youngster's contract, complete with a bumper new buyout clause.
The Stamford Bridge side fear the La Liga club could slap a £30m price tag on Isco, and Rafa Benitez is eager to sign up the Malaga star before Manchester City beat them to it.
The report claims Roberto Mancini first registered an interest in Isco towards the end of 2012, following the arrival of former-Barcelona director of football Txiki Begiristain at the Etihad Stadium.
Begiristain has an intimate knowledge of Spanish football and advised Mancini to try and sign Isco, one of the hottest prospects in La Liga.
Malaga have progressed to the last-16 of the Champions League, with Isco a key reason behind their good form, and his performances in Europe have accelerated the Spanish club's efforts to sign him up to a new contract.
The Daily Mail report a new deal for Isco would likely raise his release clause above £30m.
Malaga experienced financial difficulties in the summer, but are not thought to have any desperate need to sell this January. The club sits fourth in La Liga, and is keen to push on in the second half of the season as they look to clinch Champions League qualification for next season.