The France attacker feels that if the Liverpool striker were to sign for Madrid, it would boost him, while Sunday's match against Jamaica is not a case of him against Giroud
The European champions have been strongly linked to the 27-year-old, who enjoyed a record-breaking season with Brendan Rodgers' side by netting 31 times in just 33 league matches.
If a move to the Spanish capital were to be completed, it would be Benzema’s place that would be most immediately under threat, though the France star has indicated that he would relish the challenge the South American would bring.
Speaking to Telefoot, he said: "There is always a lot of noise and [these rumours] will definitely not be keeping me up at night.
"Competition has never been a problem for me since childhood. It makes me raise my level."
Benzema is set to play for France against Jamaica on Sunday evening, having missed Les Bleus’ two previous World Cup warm-up matches due to a slight injury issue.
In the meantime, Olivier Giroud is seen to have stolen a march on the former Lyon forward owing to his strong form, but ahead of the final rehearsal before Didier Deschamps takes his team to Brazil, Benzema does not see this as a make-or-break chance to ensure his place in the starting XI.
"It's not a game between Giroud and me," he explained. "Since I've played football, I have never got into such debates. It was the same with [Gonzalo] Higuain at Real Madrid.
"The main objective is to go as far as possible. I'll be ready for the World Cup. I have been back in training and have recovered well from my little problems."
France’s opening World Cup match is against Honduras on June 15.