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The 33-year-old currently has a contract at Barca until summer 2021 which will be extended a further year if he plays 60 per cent of their matches next season.
Inter Miami, who have David Beckham as an investor, reportedly want to bring in a big name who can appeal to the city's Hispanic fans and Mundo Deportivo report they have made an offer for Suarez.
His compatriot Nicolas Lodeiro, who plays for MLS club Seattle Sounders said in November 2019: "Luis wants to come to MLS. He likes the league. He always asks me questions about it. Hopefully he can also play here for the Seattle Sounders .
"It can be a more difficult task. I think it's only a matter of time before he is here."
Luis Suárez (Barcelona)
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The news jumps because he said MLS interests him once on the radio (RAC 1). In fact, his idea is to complete his Barcelona contract and even extend it for another year.
Suarez is the brother of Lionel Messi at Barcelona and has no intention to sell him. His idea is to stay and that of the board is to stay as long as he wants.
Suarez has once commented that he would like to know other markets and the MLS is one of those that he likes.
But Suarez believes that he still has two years of good football in Barcelona.