Julen Lopetegui (Getty Images)
Bale has been the source of constant rumours of a switch to Old Trafford after becoming disillusioned at a lack of playing time last season under former coach Zinedine Zidane.
Ahead of a pre-season fixture against Man United, Lopetegui said that the 28-year-old attacker was happy to remain at the Santiago Bernabeu.
"He's very, very happy," Lopetegui told journalists. "He's very happy to play at Real Madrid. He's happy to be here, this is a fantastic opportunity for him to show his talent.
"I've talked to him like I've talked to everyone. He's with the team, he's happy, he's in line with our goals and it's a start of a new exciting path for us that I'm looking forward to."
The former Spain national coach said that he was confident that the players in his squad were capable of filling the void left by club record scorer Cristiano Ronaldo.
"We first recognise Cristiano as one of the most important players in the recent history of Real Madrid," said Lopetegui.
"He vocalised his desire to leave and the club gave him all the facilities to do so. We wish him all the luck in the world.
"And when it comes to our players, Bale and everyone else, we are completely convinced we have the players to move forward.
"Bale is a magnificent player with qualities and we are convinced he and everyone else can fill the void."