The 18-year-old prospect has been followed by several Premier League clubs, and enjoyed an impressive trial at Arsenal last month.
He's been offered a three-year-old deal by Gunners boss Arsene Wenger, and the report claims he is set to sign the contract in the coming days.
League Two side Bristol Rovers will be due a compensation fee should the transfer go through.
They revealed talks with Arsenal and Everton were ongoing last month regarding a potential deal for Macey, and it seems Wenger has now won the race for the highly rated stopper.
He'd be a long-term project for Arsenal, with Wojciech Szczesny established as number one and Emiliano Viviano brought in on loan from Palermo as back-up for the season.
As a result, it's unlikely he would be involved in the first-team this term.