The Croatia international has frequently been linked with the Old Trafford club, while Inter Milan are also said to be interested.
However, the 31-year-old made his intentions clear after helping Barça clinch the Liga title with a 1-0 win over Levante on Saturday.
"I don't want to be anywhere else," he told Marca.
"I hope the club, the president, the coach and the fans see this the same way I do.
"I hope they tell me that I'll stay here for another three years.
"I'd like to be able to point to the three more years on my contract and to say I'll be here three more years.
"Anything can happen in football, but I am very calm about it all."
Rakitic has scored five goals and contributed six assists in 48 appearances across all competitions for the club this season.
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