The London Evening Standard reports the Gunners are exploring a move for the Newcastle United captain as Mikel Arteta looks to strengthen his options in midfield.
Arsenal held initial talks with Guimaraes' representatives last week in an attempt to understand his situation and gauge the feasibility of a deal.
An informal proposal of around £55million was then made to Newcastle, suggesting the north London club had been given encouragement on the player side to firm up their interest.
Newcastle rejected the approach, but The Chronicle now suggest that damage may already have been done, with the player's head potentially turned by the transfer pursuit.
Arsenal reportedly believe that a fee in the region of £65million could be enough to convince Newcastle to part company with their captain this summer.
Newcastle will now fear a similar scenario to the one involving Alexander Isak, who refused to play for the club after being made aware of Liverpool's interest in signing him.
There has been no suggestion that Guimaraes is ready to force through a move himself, having never previously expressed a desire to leave St James' Park.
The Brazilian midfielder is currently away at the World Cup, but his representatives have been holding separate discussions over his future at Newcastle in his absence.
Guimaraes has two years left to run on his current contract, and a new deal is not currently close to being agreed between the two parties.
There has been no direct contact between the two clubs at this stage, and an official offer has not been submitted as things stand.
It remains to be seen whether Arsenal will move to intensify their interest and follow up with an official bid.
Newcastle also face losing Sandro Tonali to north London this summer, with Tottenham pushing to complete a club-record deal for the Italian midfielder.
Spurs beat Manchester United to the £85million signing of Matheus Fernandes on Tuesday.