The Welsh international has chosen to stay at the Bernabeu after months of speculation about his future.
According to the Spanish media Don Balon, the former Tottenham star is becoming increasingly influential in the corridors of power.
It is suggested that he has urged Lopetegui to look for a new forward and thinks that Moreno could meet the requirements.
The 27-year-old player has a constant record, although not spectacular, in the Spanish top level.
"Real Madrid star Gareth Bale wants Rodrigo Moreno at the Bernabéu"
Moreno has bagged 37 goals in 135 games for Marcelino's team.
Real Madrid will face Atlético de Madrid in the UEFA Super Cup on Wednesday and Lopetegui praised Bale after he struck yesterday in a 3-1 victory over AC Milan at the Bernabéu.
He said: "I'm not going to talk about past seasons.
"The Bale we have now is committed, happy, wanting to have a great season.
"He is training very well, happy, and we are very happy with him, this has just started."
A new forward could question the place of Karim Benzema in the team.
Lopetegui, however, insists that he is happy with the experienced international from France.
"With Benzema we are happy," he added.
"He trained very well, he is in excellent shape, enthusiastic and enthusiastic.
"It will surely help us in all facets, not just with its objectives.
"He contributes a lot to the team and we are happy for what he does".
Real Madrid has been repeatedly linked with Chelsea striker Eden Hazard.
A move could still be in play, although it seems unlikely with the English transfer window now closed.
Premier League hero Paul Merson is concerned that Europe's elite looting the Chelsea stars.
"As you said about Hazard and Willian, I would put Kante there," Merson said.
"Who would not want it? If the PSG or someone comes in and says" oh, £ 100m. "
"Season tickets are sold now, the land is sold out.
"Chelsea does not have to worry about selling seats.
"Money talks and I would be very worried if I was Chelsea's coach at the moment, just because they have three big players there who could easily play at Barcelona or Real Madrid any day of the week."