The two Premier League clubs have watched the Brazil star on several occasions over the last six months and have been heavily linked with a move during the close-season.
Arsenal sporting director Edu addressed their interest in Paqueta over the weekend as he revealed a move was unlikely given the options Mikel Arteta possesses in the final third at the current point in time.
Newcastle have been linked for a move ever since they completed a deal to sign Paqueta’s Lyon and Brazil team-mate Bruno Guimaraes during the January transfer window and speculation over a possible switch to Tyneside was further fuelled when Paqueta visited the Magpies midfielder earlier this summer.
The former AC Milan attacking midfielder is reportedly keen on a move away from Lyon and Cheyrou has confessed a departure is a possibility.
He said: “We need to reduce the squad size.
“In terms of departures, we will analyse offers on a case-by-case basis but the economics will come into consideration. We will consider the offers with Jean-Michel Aulas and Vincent Ponsot in order to make the best decisions. I am here to ensure the best team possible, but there are other things to take into account as well.”
Speaking specifically about Paqueta’s possible exit, Cheyrou added: “We are prepared for every eventuality.”
Magpies manager Eddie Howe spoke about speculation over a possible move for Paqueta and his close friendship with United star Bruno towards the end of last season, saying: “Certainly, it helps to have players play at the very highest level because those relationships and opinions can be very valuable.
“I have signed players from many different sources over the years. I've never cut off any recommendation from anybody. But of course, I’d have to go through the right process of watching and analysing the player to see if he’s right for the team.”