The 25-year-old has stressed that any player who can improve the Blancos squad has a place at the Santiago Bernabeu, and dismissed rumours linking him with a move away
The 25-year-old struggled to assert himself in Jose Mourinho's starting line-up last season, and was behind Xabi Alonso and Sami Khedira in the pecking order for a midfield spot.
Meanwhile, Modric looks likely to finally leave Tottenham Hostpur after the north Londoners failed to seal a Champions League spot for the coming season, with the Santiago Bernabeu seeming to be a likely destination.
However, Granero would not consider leaving the club even if the former Dinamo Zagreb playmaker arrives in the Spanish capital, and is determined to fight for his place.
"Every year great players come and great players go," he is quoted as saying by AS. "What is most important is that the team is strengthened.
"Improving the squad every season is complicated. They will be working hard for it, and we are always bringing in good footballers.
"I don't know whether it will be him, someone else or nobody, but we will always welcome players that improve Real Madrid with open arms.
"I haven't thought about leaving and I have not thought about having the same role as last season. I want to have more importance, as all players do.
"Having a greater role does not mean changing team. It can be done here and I will train hard. I hope to carve out a niche for myself. I have matured a lot over the last year."
Granero has been at Madrid since 1996, but spent two years at Getafe between 2007 and 2009, before returning to the Bernabeu.