Gallagher could be on the move from Chelsea in the ongoing transfer window and has serious interest from Tottenham Hotspur and West Ham United.
Newcastle have had a long term interest in Gallagher and he is a player that Magpies boss Eddie Howe rates.
However, Newcastle have cooled their interest in the midfielder as they feel no need to add him to the squad after signing Sandro Tonali.
Big money was splashed to sign Tonali from AC Milan and as a result, Newcastle are not moving for Gallagher.
The club are trying to sign Southampton full-back Tino Livramento, while Harvey Barnes has just arrived.
And with financial fair play considerations, it is unclear what further additions Newcastle will make before the transfer window closes.
There could also be a number of departures from St James’ Park, with goalkeeper Karl Darlow one player who is attracting interest.