The Magpies value their captain above £80m, well clear of Arsenal's reported opening offer of around £70m, leaving the Gunners weighing an improved bid after their first approach fell short.
Guimarães himself flew out of Brazil on a commercial flight on Sunday to join his Newcastle United team-mates at their pre-season camp in La Manga, where talks with incoming manager Matthias Jaissle are scheduled; he still has two years left on his contract, plus a club option for a further year, and Newcastle remain reluctant to sell.
The 28-year-old has told the club he wants to make the move to Arsenal, and the north London side are currently the only club believed to be in the frame.
Newcastle have already banked around £100m from Sandro Tonali's move to Tottenham and roughly £75m from Anthony Gordon's switch to Barcelona this summer, so Guimarães would not arrive at the Emirates cheaply even with those funds already raised.
He has made 195 appearances and scored 31 goals since his £40m transfer from Lyon in January 2022, and recently paid tribute to departed head coach Eddie Howe on social media, calling him "king of this club" after Howe's Newcastle exit amid the swirl of Arsenal interest. Howe's departure, in turn, has left incoming boss Jaissle facing the prospect of losing his most influential player before taking charge of a single competitive match.
Adding to the sense that a move is gathering pace, The Mag reports that stadium banners showing Guimarães posing in Newcastle's new kit have been quietly taken down around St James' Park and replaced with images of other players.
Newcastle insist advertising material is changed regularly and the timing could be coincidental, but supporters hoping for one more season of Guimarães in midfield are growing increasingly uneasy about what the change might signal. At 28, Guimarães is arguably approaching the peak of his market value, giving Newcastle an added financial incentive to cash in now rather than risk his valuation declining over the coming seasons.