Alonso, who joined Madrid in 2009 after five years in the Barclays Premier League with Liverpool, believes Modric needs to be given time to settle in and is convinced the Croatia international will be a success at the nine-time European champions.
"I don't think it's pressure. He plays in a position where we have several players and he's adapting to a new club and a new league. It took me a while to adapt on my return to La Liga," Alonso told reporters on Tuesday.
"But he's integrated very well, he's a fantastic guy and a great player. I've no doubt that he's going to be an important player."