The Magpies are one of several Premier League clubs said to be keen on a move for the attacking midfielder and there is also interest from major clubs in Scotland.
The 16-year-old is the son of former Robins assistant manager Jamie McAllister, who was recently named as number two to former City boss Lee Johnson at Scottish Premier League club Hibernian.
McAllister junior has progressed through the Robins academy ranks and made his Under-23s debut at the age of 15 in a 2-0 defeat against Queens Park Rangers last October.
Speaking after the game, Robins professional development coach Ali Hines praised the progress of McAllister and fellow debutant Ephraim Yeboah, telling the club’s website: “It’s fantastic for those boys.
“Their attitudes and quality of performances have been really good, so it’s a credit to the schoolboy program as well who have been coaching and working with them.”
The youngster is seen as one of City’s brightest prospects and his rapid progress through the club’s academy setup has attracted the interest of several clubs from higher up football’s food chain.
A BristolWorld source has indicated McAllister is on the radar of a number of Premier League clubs, with Newcastle said to be the latest to show an interest in acquiring his services as they look to enhance their academy ranks this season.
However, the Magpies could face competition from clubs in Scotland if they decide to make a move for the youngster.