The Daily Mail revealed on Thursday that Arsenal had held talks with Guimaraes' representatives, only for Newcastle United's hierarchy to make clear that the 28-year-old is not for sale. A new proposal is now being prepared and will be presented to the Magpies, though their stance is expected to remain the same.
Guimaraes is currently at the World Cup with Brazil. He has not told Newcastle he wants to leave, but the circulation of his name among Premier League rivals has raised alarm inside St James' Park.
The midfielder has two years remaining on his contract and it is not yet known whether he is looking to move on or negotiate an extension at the club.
Manager Mikel Arteta is keen to add quality in central midfield ahead of Arsenal's title defence, and Guimaraes has emerged as one of his leading targets. The Gunners had initially been linked with the player before the current window opened, and their pursuit is now understood to have moved into a more active phase.
Newcastle's position has been consistent throughout — their captain is not available — but Arsenal's willingness to submit a second formal approach suggests they believe there is room to negotiate, particularly with Guimaraes' contract situation giving his club limited leverage in the longer term.
Whether a third approach will follow if this bid is again rejected remains to be seen, but Arteta's determination to strengthen in the engine room before the new season is clear.
Guimaraes' performances for Brazil at this summer's tournament have only enhanced his standing, and are likely to sharpen Arsenal's resolve to push through a deal.