The Gunners are expected to put forward an initial £70 million proposal but are understood to be ready to return with an improved offer if their approach is rejected.
Sources are indicating that Guimaraes is keen on the move, and that personal terms are agreed. Arsenal are determined not to miss out on another priority target.
Arsenal have already seen one major transfer plan fall through this summer after Morgan Rogers completed a £117 million switch from Aston Villa to Chelsea.
The north London club had valued Rogers at around £80 million and believed that figure would be sufficient, only to be beaten by Chelsea's significantly higher offer.
That experience has strengthened Arsenal's resolve to act decisively for Guimaraes.
Sources suggest the club may be willing to increase their offer towards a package worth over £80 million, including add-ons, but that would be viewed as the very upper end of their valuation.
Newcastle, however, may seek a fee closer to £100 million.
The Magpies are likely to use Sandro Tonali's move to Tottenham, worth a total package of £100 million, as a benchmark in any negotiations.
Despite Arsenal's interest, Newcastle's position remains unchanged.
As of Thursday night, the club insisted they had no intention of selling Guimaraes during the current transfer window.
A formal approach from Arsenal for the Brazil international is anticipated very soon.