The Championship side are hoping that the forward can improve their bid for promotion.
Aitor Karanka's men currently sit second in the Championship, but find themselves in a group of five teams that are separated by just four points.
With last year's play-off final disappointment - where they were beaten by the Canaries - still in the back of their minds, it appears that Karanka is determined to ensure that they book their place in the top flight by finishing in the top two, and wants Jerome to be the man to lead them towards that goal.
The 29-year-old - who spent a brief spell at the Riverside Stadium over a decade ago - was crucial to Alex Neil's side's promotion push last season. He scored 18 goals in 44 appearances.
However, he has found life in the Premier League much tougher, with only two goals to his name this season. And with Lewis Grabban staking a claim for a regular place in the side with the equaliser against Arsenal, Jerome may decide that he needs to move on, should he find his place in the squad under serious threat.