Reuters says United are favourites to land the Brazil international, who is ready to leave St James' Park this summer.
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Guimaraes, 28, is seen at United as a readymade successor for his Brazil teammate Casemiro.
United and Newcastle are happy to strike terms with a fee of £69m raised as a likely settling point.
Real Madrid are also interested, as they seek to rebuild their midfield, though United are much further down the road in striking terms,.
Guimaraes is now in his fourth year at St James' Park, having arrived in January 2022 from Olympique Lyon for £40m.