The attacking midfielder is down the pecking order at Manchester United, and is being allowed to leave.
Italian reports and the Manchester Evening News state that Pereira will sign on loan for the rest of this season.
The deal includes an option to buy for a specific price, while both clubs will share the player's wages.
Their manager Simone Inzaghi added: "I know him, he is a quality player who can give us a big helping hand. I don't want to talk too much about players who haven't signed yet.
"We'll see if he arrives or not."