It is unclear whether the 40-year-old former Chelsea striker has been contacted regarding the role of manager, caretaker manager or coach.
McLeish departed the City Ground by mutual consent on Tuesday having only taken the reins on 27 December following the departure of Sean O'Driscoll.
The Scot was reportedly unhappy with Forest's transfer dealings ahead of the closure of the January window when they failed to bring in any new players, the deal to bring in Peterborough winger George Boyd falling through at the last minute on Thursday because of an issue with the player's eyesight.
McLeish, 54, remained in charge for Saturday's 2-1 defeat at Birmingham - his fourth loss in seven matches since being appointed - but left the Championship club after just 40 days at the helm following talks with Kuwaiti chairman Fawaz Al-Hasawi.
McLeish said: "I am extremely saddened to be leaving after such a short period but even so it has been a privilege to be manager of such a fantastic football club."
Former Forest manager Billy Davies and ex-Southampton boss Nigel Adkins have also emerged as possible candidates.
Hasselbaink was brought to Forest by Steve McClaren in 2011 and then worked under O'Driscoll this season as first team coach, but departed last month after terminating his contract by mutual consent.