Real have signed Thibaut Courtois, Alvaro Odriozola, Vinicius Junior and Mariano Diaz to bolster the first-team this summer, with the most recent addition, Mariano, to be the last, despite intense links with the Belgium international.
Reports suggested that the club could break the bank for the forward, after Hazard hinted at a move to the Spanish capital, but Lopetegui does not expect such a deal to be done.
Instead he insists that the only business Madrid are likely to do before the transfer window closes on Friday is loan out striker Borja Mayoral, who is reportedly set to join Levante.
"Now with Mariano, the Real squad is closed," he told reporters.
"Just Mayoral could leave on loan. He needs to leave to fight for minutes. We respect him. Once Mariano is in the squad, he feels he's going to have
Real's recruitment of Courtois has led to questions over who will wear the No.1 shirt at Santiago Bernabeu.
Keylor Navas held the shirt for the entirety of last season, and Courtois has yet to make his La Liga debut for the club.
Lopetegui, though, says he is unwilling to commit to naming his No.1 in public.
"I'm not going to say who's my starter goalkeeper. I have great solutions in that position. I have full confidence in
Real's Luka Modric beat out former team-mate, and new Juventus signing, Cristiano Ronaldo to win the UEFA Player of the Year award on Thursday at the Champions League group stage draw.
Ronaldo's agent, Jorge Mendes, was fuming with the result, insisting that his client should have won the honour, but Lopetegui maintains that he will not be drawn into such matters.
"I'm not going to talk about the Mendes quotes," he added. "I'm very happy for Modric winning the trophy."