The France international signed a new contract with the European champions earlier this month and is ready for renewed competition for a starting berthKarim Benzema has insisted that he would not be concerned if Real Madrid were to sign a new striker before the close of the summer transfer window.
The France international put pen to paper on a new five-year deal with the Santiago Bernabeu club this summer, ending speculation over his future.
However, the European champions are still being heavily linked with a move for Monaco attacker Radamel Falcao - and Benzema insists that he would welcome the extra competition for a starting berth.
"For me, Real Madrid are the biggest club in the world and it's normal that they'd want to sign a striker," the forward told reporters.
Madrid beat Sevilla 2-0 on Tuesday to claim Uefa Super Cup glory and Benzema is confident that Carlo Ancelotti's reinforced squad can complete a clean sweep of trophies this season in light of the summer signings of Toni Kroos and James Rodriguez.
"It's very nice to win this title, with good players having a good game," the 26-year-old continued.
"Toni Kroos and James Rodriguez are great players who will help the team. We have many good players in attack and they'll gradually work together to help the team.
"We did a great job [against Sevilla] and we are very happy with this title. I am very pleased and happy at Real Madrid. I'm going to continue working to win many titles here.
"It's possible to win six trophies, we will work for it. We have many players, we are stronger than last year. Now we have two senior teams."