Bale's last outing for Los Blancos saw him come off the bench to score twice in a match-winning display in the Champions League final, but immediately after the game he suggested that he could leave the club in search of more regular first-team football.
Lopetegui has since replaced Zinedine Zidane in charge of Madrid, though, and Bale is keen to speak to the former Spain boss to determine how big a role he will play in his plans.
The majority of Madrid's players are due to return to training next week, and Sky Sports News reports that Bale's representatives will also fly out to hold talks with club president Florentino Perez.
Madrid are understood to want to keep hold of Bale following the sale of talisman Cristiano Ronaldo to Juventus, although they have also been linked with the likes of Neymar, Kylian Mbappe and Eden Hazard.
Manchester United are thought to be in advanced talks with Madrid over a move for Bale, although the likelihood of any deal could rely on whether he is given the reassurances he is after by Lopetegui.