The striker has not played since last February when he suffered a serious knee injury in a match at the City Ground against Wigan Athletic.
The Sun report: "The good news is he is close to a return and could feature at Derby on Saturday."
Assombalonga was Forest's top goalscorer before his injury and the club have struggled to replace him since.
Their highest scorer this season is loanee Nelson Oliveira, who has nine goals, with defender Matt Mills following with five. Assombalonga had 15 before his injury last season.
The striker himself is less bolshy about next weekend's fixture, but believes he is on track, telling the paper: "I don’t know how far away I am. I have dipped back into full training with the other lads which is good. I feel all right."
When he does return it will be a significant boost to Forest, and an appearance against Derby would be a real confidence boost for the out of form side.
It would also be unfortunate timing for Dougie Freedman, who was fired at the weekend, after being without Assombalonga for the majority of his tenure as boss.