Coutinho is available after failing to revive his career on loan at Bayern Munich, who have decided against activating a permanent option.
The Bundesliga winners did negotiate a short-term extension with Barcelona to keep the Brazilian for the remainder of their Champions League campaign, which kicks back in to gear against Chelsea this evening.
A string of clubs have been credited with an interest in Coutinho including Chelsea and Leicester City.
Arsenal appear to be the frontrunners, however, after reports emerged that the 28-year-old and his representatives had visited London Colney for talks.
Coutinho would likely join on loan instead of a permanent deal due to the Gunners' limited transfer budget, which was given a boost after they lifted the FA Cup and booked their place in next season's Europa League.
According to Sport, the Barcelona flop has slammed the brakes on a potential move, however, by informing Nou Camp bigwigs that he does not want to consider offers while Bayern Munich's Champions League campaign is in progress.
He is eager to end his loan spell at the Allianz Arena by winning the competition to leave with three medals, having helped in the Bundesliga and DFB-Pokal successes.
Coutinho's agent Kia Joorabchian, who is pals with Arsenal chief Edu, previously admitted his client would like to focus on the Champions League before thinking about a move.
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"Because the Champions League will run until August 23, it will be difficult for players like Coutinho to make any commitments or moves pre that date," Joorabchian said.
"Because he has the Champions League at the moment, they have to qualify past Chelsea. And then he has got to play Barcelona, believe it or not.
"For him to make a commitment pre having finished the Champions League.
"He loves playing in the Premier League, he is adored playing in the Premier League and that is one of his priorities.
Arsenal target Philippe Coutinho wants to finish the Champions League before moving clubs (Image: GETTY)
"He is not at all against staying at Barcelona."
Arsenal legend Martin Keown is not convinced by a swoop for Coutinho, who has struggled to replicate the form that earned him a £142m move to Barcelona from Liverpool in January 2018.
"Coutinho has been linked with virtually everybody and seems, if I am honest, a bit unsettled," Keown told the Daily Mirror.
"I think Willian is a safer bet. He's in the capital, he knows the Premier League very well and he's a top performer. I think it's a huge loss for Chelsea."
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