Rice, 20, last week pledged his international future to England despite having three caps for the Republic of Ireland in friendlies.
The London-born player will make only his 60th West Ham appearance against Fulham on Friday night, but Pellegrini insists he is ready for the call-up when it comes from Three Lions boss Gareth Southgate.
Eric Dier and Jordan Henderson are Southgate's current picks to sit in front of the back four although Pellegrini rates Rice above both of them.
He said: "I think he is ready to play for England. I think we are just starting the development of him as a player, but at this moment his performances are better than every holding midfielder.
"At least I am taking about the English players. Maybe there are other foreign players in big teams that are also playing well, like Fernandinho, but I repeat, we are just starting to see what will be with Declan in the future.
"He is improving in a lot of different things in that position. Maybe he must improve more and have a better view of the pitch, but he has such good technique that he never misses a pass.
"He is always keeping his position in the correct moment, so as young player he will always be learning more things, but at this moment I think he is a complete player."
Pellegrini was in charge of Argentinian side River Plate when a young Javier Mascherano came through the ranks.
The Chilean claims Rice reminds him of the former Barcelona and Liverpool midfielder.
"It is difficult to compare different players in 20 years of management, but Declan is a very good player," Pellegrini added.
"I worked with so many young players. I started with Javier Mascherano when he was 17 and he was similar to Declan in his mentality.
"The mentality when they are 17 or 19, it seemed they had the mentality of a 35-year-old. When you have 17, 18, 19-year-olds arrive in the first team, playing in the first team changes a bit your mind and you think that you are ready.
"But, in the case of Declan, he knows that he is just starting and that is important."