Tottenham Hotspur boss Mauricio Pochettino is still Real Madrid's first choice to replace Zinedine Zidane, but the European champions want to sort out their coaching position before the start of the World Cup.
Zinedine Zidane shocked the world when he announced that he will step down as the Real boss just days after their UCL victory.
Other candidates in the running - but with no concrete links yet - are former Arsenal boss Arsene Wenger, Juventus manager Massimiliano Allegri, and Hoffenheim coach Julian Nagelsmann.
The Real hero is now in charge of the club's Juvenil A squad, but Murcia president Victor Alvarez believes he's set for a dramatic promotion.
"Guti is going to coach Real Madrid so he can not coach Murcia".
However, the Spaniard now looks set for a much higher-profile job, with the Murcia president admitting that Zidane's resignation has scuppered his chances of appointing Guti.
Conte also feels a "coach with strong and decisive methods" would not be welcomed in a settled dressing room, which has seen him cool interest in the Champions League winners.
It has been claimed Real Madrid are not keen to drag out the process for too long and are aware that the media scrutiny on the club is only going to increase if the new coach is not appointed soon enough.
Guti scored 77 goals in 542 games for Madrid between 1995 and 2010, winning five La Liga titles and three Champions League trophies, while drawing mixed reviews from pundits and coaches for his carefree attitude on and off the pitch.