Chelsea were heavily linked with a move for Zenit midfielder Leandro Paredes but missed out on his signature to Paris Saint-Germain.
After the exit of Cesc Fabregas to Monaco earlier this month, The Blues have been left short of options in midfield and Rakitic has since been mooted as their top transfer targte.
With Netherlands international Frenkie de Jong joining Barcelona from Ajax for an initial £65m fee at the ene of the season, the Spanish side will reportedly need to balance their books by selling at least two players.
However, the Croatia international has made his intentions clear, despite the possibility of limited playing time if he remains at the Camp Nou.
"I want to be here, and if I can renew, be here for a few more years," he said, as reported by Onefootball.
"I'm very happy here, everyone knows it, most of all the president. I don’t have to say anything else."
Quizzed about his position in the team with De Jong set to link up with the club in the summer, he said: "That is a good question for the coach or for the president. The people who know me know that I am only here to play.
"I approach it with calmness and a lot of desire. I am 30 years old, and I am in the best moment of my career. I want to enjoy football and Barça."