Bruno Guimaraes
Image caption, Bruno Guimaraes was Newcastle United's top scorer in the Premier League last season with nine goals
The clubs are understood to be in formal discussions regarding the midfielder, with previous discussions being done through intermediaries.
Guimaraes, 28, wants to join the Premier League champions.
Whether a deal will be agreed remains to be seen, but those involved feel the transfer is moving towards a resolution.
BBC Sport previously reported that Arsenal would need to increase a £70m bid they made through intermediaries last month.
One source at Newcastle has since said the club have rejected an offer from Arsenal.
Although Arsenal have failed with an unspecified offer - neither side has disclosed the amount - it is expected they will return with an improved bid.
Guimaraes has travelled to Spain for Newcastle's pre-season training camp in La Manga, as planned, following his post-World Cup break.
The Brazil midfielder has been a priority target for Arsenal as the club look to further strengthen after winning the Premier League last season.
Arsenal manager Mikel Arteta would not be drawn directly on Guimaraes over the weekend, but said the club were "very active" and "very ambitious in what we want to do".
"We need to increase the competition internally," he added.
"We need to make sure we identify the things that we don't have in the team."
Newcastle finished 12th in the Premier League last season, with Guimaraes providing nine goals and eight assists across all competitions.
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