Lopetegui and the Spain squad are now at their training base in the southern Russian city of Krasnodar.
Spain are among the favourites to win the World Cup after an nearly flawless qualifying campaign, and he will be hoping that the announcement does not overly unsettle his squad just before the competition gets under way.
Julen Lopetegui on Bale in 2015, "A player at Real Madrid has to give 100% all the time".
The Independent is reporting that the Spanish giants are in no rush to resolve the Wales international's situation despite the uncertainty about his future this summer.
His name had been briefly mentioned among many others as a possible successor to Zidane, who stepped down on May 31 after leading the club to a third straight Champions League crown, although a move seemed highly unlikely.
Speaking just three weeks ago after signing his new Spain contract, the former Porto boss said: "I'm grateful for the confidence placed in me and in my staff".
The 51-year-old took over as Spain coach in 2016 following the retirement of Vicente Del Bosque.
Indeed, Spain are still unbeaten under the Basque after 20 matches including friendlies.