Rakitic joined the Catalan giants this summer for a reported fee of €20 million after a magnificent campaign with Sevilla.
The Croatia international says he has been training with Messi recently and admitted he has been in awe of the four-time Ballon d'Or winner.
"I trained a few times with Leo because he joined the team later due to the World Cup," he told 24sata. "Sometimes in training I stop and watch him, he is miraculous. I admire him and I learn from him.
"He impresses me with everything he does. He behaves normally, as if he isn't such a big star."
The 26-year-old said he in constant conversation with coach Luis Enrique, who has told him he admires him greatly.
"I haven't spoken specifically about positions with Luis Enrique because we are still in training," he added. "It will take time. He talks to me very often, to him the details are very important, he cares a lot about the little things.
"He told me that he realised that I was great when I was playing against his former club Celta."
Rakitic also praised 18-year-old team-mate and compatriot Alen Halilovic before stressing his excitement at getting the season underway.
"Alen thrills everyone. Everybody is talking about him and praising him. The coach likes him and he is still with the first team. In training he is great.
"I can't wait to start. I think it's great for Croatian football to have three players playing in big clubs. I will lead a big fight for the title against Real Madrid and Atletico Madrid. Playing against Mandzukic and Modric will be very interesting."