The Gunners are rumoured to have seen a £70M bid rejected by the Magpies yesterday after weeks of speculation over when they would launch an official bid for the 28-year-old
Guimarães has already told Newcastle he wants to leave, but the club are pushing for around £80M to consider a sale, with two years still left on his contract and a club-held option for a third.
The Brazil international is currently away on a preseason training camp with the managerless Magpies in Spain, but BBC Sport have updated the situation, by confirming formal talks are now in place.
"As far as we understand the clubs are in formal talks. There's been a claim of Newcastle rejecting an opening bid from Arsenal, and the player is at the training camp in Spain, so I think this one is going to run a little while longer.
"Arsenal, as it's been reported, are confident still of signing Guimaraes."
Newcastle are pragmatic over the chances of retaining their skipper, but after bringing in £100M for Sandro Tonali last month and £125M for Alexander Isak in 2025 - the latter after a transfer saga with Liverpool - BBC sources claim they want to avoid a repeat.
"Whether this turns into an Alexander Isak-style saga, I'm not so sure.
"I think we should have a resolution one way or another far more swiftly than that.
"It feeds into Eddie Howe's wider decision to step down. If Guimaraes is to go then Newcastle will have lost four key players in less than a year. That is a huge rebuilding job for any manager."