Sky Sports say the Premier League club have come back to the table with a bid of £17.3m for the Belgium international.
Martin O'Neill spoke after yesterday's victory over Falkirk, where he insisted the player was not for sale.
Asked directly if he wants to keep Engels at Celtic amid the interest from Forest, O'Neill said: “Absolutely… No question about it.
"I'd want it rebuffed [any transfer bid] unless it was £100m."
Read more:
Now, it seems Forest are unlikely to give up before the 5pm transfer deadline in England.
Reporter Anthony Joseph wrote on X: "Celtic have rejected an improved offer of £17.3m from Nottingham Forest for midfielder Arne Engels.
"#CelticFC have told #NFFC that the Belgium international is not for sale in this window."