Mikel Arteta is eager to strengthen his midfield options and views the 28-year-old as an ideal partner for Declan Rice in the heart of Arsenal's engine room.
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Guimaraes, under contract until 2028, has been a key figure for Newcastle since joining from Lyon in 2022 but is now believed to be seeking a fresh challenge and continued Champions League football.
Newcastle are reluctant to lose their captain following the departures of Sandro Tonali and Anthony Gordon, although discussions over his future have already begun.
Arsenal are now considering a move, with a fee of around £60 million expected to open negotiations.