According to the Express, the Gunners have beaten off competition from their rivals and are set to land the midfielder before the end of the summer transfer window.
It is claimed that Arsene Wenger, who refused to discuss a move for the midfielder in his press conference, has agreed a fee of around £12m for the midfielder.
The Frenchman has been on the market and admitted that he could buy another midfielder to cover for the loss of captain Mikel Arteta. He has been linked with various players over the summer. The latest in the rumour mill is Sporting Lisbon midfielder William Carvalho, with reports suggesting that the north London club have made a fresh £20m bid for the player.
Rabiot is a Wenger-type of player, as he is versatile and can play in midfield or in defence. He would provide good cover at a number of positions in the Arsenal squad.
The 19-year-old midfielder is on the final year of his contract at the Ligue 1 club and is unwilling to negotiate a new deal.
PSG manager Laurent Blanc has expressed his keenness at retaining the player, but revealed that Rabiot has rejected a new deal and is set for a move away from the club.
Meanwhile, Arsenal face Premier League newcomers Leicester City on Sunday and defender Laurent Koscielny is not taking anything for granted. He is expecting it to be a tough evening and is hoping that Arsenal can continue their good run of form and pick up the three points.
"No game is easy in the Premier League. We need to be fit, to prepare well mentally and physically. It's a fight every weekend and against Leicester it will be hard," Koscielny told Arsenal's official site.
"We need to prepare well for the fight but we need to play our game with our qualities too. Leicester are newly-promoted but they want to show all the people that they can stay in this league. It won't be an easy game but we need the three points," the French international added.