The Reds have been active in recent transfer windows, signing 30 players since winning promotion to the Premier League last season.
Central defenders Willy Boly and Moussa Niakhate arrived last summer to bolster Forest's defensive ranks, although the latter has been restricted to just two appearances due to injury issues.
Steve Cooper's side also recruited centre-back Felipe from Atletico Madrid on the final day of the January transfer window.
Despite bolstering their backline, Forest have struggled defensively this season, conceding 42 goals in 24 league games - only Bournemouth have shipped more goals in the top flight.
With Forest still keen to add to their defensive options, The Sun are reporting that they are keeping tabs on Omobamidele.
The report claims that the Premier League club have sent scouts to watch the young defender in action as they consider a potential summer move.
The Norwich academy graduate has featured in 23 league games for the Canaries this season, chipping in with one goal.
With David Wagner's currently one point adrift of the playoffs, Omobamidele is hoping to help the Canaries win promotion to the top flight.
However, Forest could also present the Republic of Ireland international with the opportunity to play Premier League football if they can stave off relegation this season.
The Reds may view Omobamidele as a potential replacement for Steve Cook, who is nearing the exit door at the City Ground.
Cook made 12 top-flight appearances before the World Cup break, but he has been left out of the club's 25-man Premier League squad for the second half of the season.
The former Bournemouth defender has less than 18 months left on his contract, and he could be allowed to depart in the summer transfer window.
Forest are currently sit four points above the drop zone, but after losing 4-0 to West Ham United at the weekend, they will be looking for a response when they face relegation rivals Everton on Sunday.