Suarez needs to do more - Benzema
Benzema netted 24 goals in all competitions last term as Real won the UEFA Champions League and Copa del Rey.
La Liga glory frustratingly eluded them, though, as city rivals Atletico Madrid - who they beat in the final of Europe's premier club competition - triumphed.
Real are expected to bolster their squad in the close-season as they look for their first league title since 2012.
And Liverpool star Suarez - who scored 31 goals in 33 Premier League appearances as his team finished second last season - is reportedly on their hit-list.
However, Benzema, who said he was unconcerned at reports of the club's interest in the Uruguayan, believes the 27-year-old needs to do more before earning a transfer to the Bernabeu.
"I sleep well, wake up as well. Everyone can come and arriving in Madrid is the best," Benzema told Marca.
"I work every day to play in Madrid.
"I have no special pressure, (Suarez) is a great player and has had a great season, but in football, you have to have several great seasons.
"He's a great player, and if he comes, he'll help us."