Both Premier League clubs have been linked with the Sevilla striker.
However, the same report suggests Liverpool hold an interest in the Frenchman and are preparing a £10 million offer.
Gameiro assisted the fastest goal in Europa League history last week, with Newcastle chief scout Graham Carr reportedly there to witness the feat. The 27-year-old also then added a goal of his own during the same encounter.
Liverpool's interest in Gameiro, though, may wane due to the fact that Divock Origi is due to link up with the Anfield outfit next summer. The Sunday People's report mentions this as well as a £10m bid, perhaps contradicting itself.
Whether the Reds are indeed interested or not, it is Newcastle who certainly harbour greater need for a striker right now. And it would be no surprise to see one extra number added to their French contingent.
Perez has impressed this season, surpassing expectations at St James' Park in a manner that has attracted interest from two of the Premier League's big guns.
The Magpies travel to Merseyside later today to face Everton at Goodison Park, while Liverpool visit Swansea City on Monday night.