The bid was received on Wednesday morning hours after reports of the London club's interest in the 26-year-old emerged.
Press Association Sport understands that the Magpies value last season's 23-goal leading scorer at closer to £20million, although may yet be prepared to settle for somewhere between the two figures.
However, they will not consider doing business with Fulham or anyone else until they have a replacement lined up amid speculation that they have an interest in Liverpool's Divock Origi.
Manager Rafael Benitez is prepared to sacrifice Gayle, who he bought for £10million from Crystal Palace last summer, after a recent drop in form.
He has already drafted in Stoke's Joselu in a £5million deal and has admitted he is looking for a different type of striker to complement the Spaniard.
Benitez has been forced to rebuild for the Premier League on a budget at a time when other clubs are investing heavily, and is having to free up resources - Emmanuel Riviere and Siem de Jong have left the club in the last week or so and Grant Hanley could soon join them - to open the door for further incomings.
Source : PA
Source: PA