It is understood that Hibs have agreed a €130k (£109k) fee with the Robins for the 16-year-old.
McAllister is set to put pen-to-paper on a three-year deal which will keep him at Easter Road until 2025.
A sell-on clause has been included as part of this agreement.
According to a recent report from Football Scotland, Celtic and Rangers were both keeping tabs on McAllister’s progress last season.
However, as per this latest update, McAllister has turned down the chance to potentially seal a move to these two aforementioned clubs in order to link up with former Robins manager Lee Johnson at Hibernian.
McAllister was on a two-year scholarship at City but is now set to embark on the next stage of his career in Scotland.
The midfielder’s father Jamie is currently part of Johnson’s coaching staff at Hibernian.
Whereas McAllister did feature at Under-23 level for the Robins last season, he wasn’t handed his senior bow by manager Nigel Pearson.
Pearson’s side will be hoping to make a positive start to the new term in the absence of McAllister when they face Hull City on July 30th.
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With McAllister set to leave the club, it will be intriguing to see whether he will be able to force his way into Hibernian’s side in the future.
Instead of following in the footsteps of Alex Scott and Ayman Benarous who have both featured for the Robins’ senior side after emerging from their academy, McAllister has decided to take a different route with his career.
By including a sell-on clause as part of this deal, City will be able to secure a reasonable amount of money if the teenager makes another move.
Having resolved McAllister’s situation at the club, Pearson’s attention is now likely to switch back to identifying targets ahead of the 2022/23 season.