It has been reported that the clubs have agreed a fee for the 21-year-old and the Oakwell outfit are about to start talks on personal terms.
The Liverpudlian striker has made just one start for the first-team, at home to Blackburn last season, and Kevin Keegan has already said that he will not offer him a new contract when his current deal ends this summer.
Shuker scored once in 15 starts on loan at Rochdale before Christmas, and has just returned to City from a loan stint at Hartlepool, where he had an identical record.
Pools had hoped to tie up a permanent deal themselves before Second Division rivals Barnsley stepped in.