The Gunners are ready to test Newcastle's resolve to keep hold of their superstar Brazilian midfielder.
The Magpies had Guimaraes under contract until 2028, but could be vulnerable to a bid if they do not qualify for the Champions League.
Arsenal are already in advanced talks with Real Sociedad midfielder Martin Zubimendi, but it is possible they try to sign both him and Guimaraes with Jorginho and Thomas Partey both set to leave as free agents.
The Gunners have been pushing to sign Zubimendi in a £51million deal after he snubbed a move to Liverpool last year.
Guimaraes is into his third full season at St. James' Park after signing from Lyon in 2022.
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He has since made 144 appearances for the Magpies, scoring 20 goals and providing 24 assists.
The 27-year-old also captained the club to victory in Sunday's Carabao Cup final against Liverpool.
After the final whistle, the fan favourite broke down in tears on the pitch at Wembley Stadium before sending an emotional message to supporters.
Having composed himself, Guimaraes told Sky Sports: "It's all for these fans. They deserve everything. When I first came here I said I wanted to put my name in history.
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"We can now say we are the champions again. This is one of the best days of my life.
"I don't have any words. It's the best day of my life. For them [the fans] it's like the World Cup.
"People have grown up and not seen us as champions. My first year as captain of this club and it's one of the best days. This is unbelievable.
"This is my second home. We are making history. Some day when I leave this club I want the fans to sing my name the way they do to (Alan) Shearer. He text me before the game. I'm so emotional today."
Newcastle's win over Liverpool ended their agonising 70-year wait for a major domestic trophy.
Goals from Dan Burn and Alexander Isak secured their first silverware since winning the FA Cup in 1955.
Guimaraes had previously had a release clause included in his Magpies deal.
However, the £100million clause is understood to have expired last summer in a blow to Arsenal's hopes of a deal.
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The Gunners have also been urged to sign his Newcastle team-mate and long-term target Isak in the past.
Isak also has three years left on his contract, which currently expires in the summer of 2028.