The 25-year-old is widely expected to depart Elland Road this term after his 11 Premier League goals helped the Whites stave off relegation to the Championship on the final day of the season.
Arsenal are thought to be at the head of the queue to sign Raphinha, who was initially expected to sign for Barcelona having agreed personal terms with the Brazil international.
However, Leeds are refusing to budge on their £65m asking price, and Barcelona's long-running financial difficulties have therefore seen them lose ground in the race for the winger.
According to transfer expert Fabrizio Romano, Arsenal are now hoping to take advantage of the situation by scheduling another meeting with Jesse Marsch's side over a possible deal.
The Gunners are already believed to have seen one bid for the former Rennes man rejected, and Leeds are still demanding a fee of £65m to part ways with their star attacker.
Romano adds that Barcelona remain in dialogue with Raphinha's agent Deco, but the Catalan giants are yet to approach Leeds with a new bid.
Tottenham Hotspur and Chelsea also continue to be linked with a move for Raphinha, who has two years left to run on his contract at Elland Road.
Since arriving from Roazhon Park in the summer of 2020, Raphinha has made 67 appearances for Leeds in all competitions, scoring 17 goals and setting up 12 more in the process.
Raphinha could potentially arrive as Arsenal's fifth signing of the summer transfer window, with Mikel Arteta's side conducting their business early before pre-season begins.
Marquinhos and Fabio Vieira were both early acquisitions from Sao Paulo and Porto respectively, and the Gunners also confirmed the arrival of goalkeeper Matt Turner from New England Revolution on Monday morning.
A £45m deal is also believed to have been struck with Manchester City for the transfer of Gabriel Jesus, who has agreed personal terms on a five-year deal until the summer of 2027.
Jesus is now expected to travel to London and undergo his medical this week before an official announcement, which would make him the fourth new face through the door at the Emirates Stadium.
Ajax centre-back Lisandro Martinez is also said to be on Arsenal's radar as Arteta seeks to boost his defensive ranks, and the Argentine could now be the subject of an improved offer from the North London club.
Interest in Martinez comes amid reports claiming that Marseille are still trying to sign William Saliba on a permanent deal, but Arsenal are now said to be in positive contract talks with the 21-year-old.