This is an improved bid from the Premier League club.
Speaking after Celtic's victory over Falkirk, Martin O'Neill made it clear that the Belgian international is not for sale.
When asked about the interest from Forest, Mr O'Neill said: "Absolutely… No question about it.
"I'd want it rebuffed [any transfer bid] unless it was £100m."
Despite the refusal, Forest are expected to continue pursuing the player before the transfer window closes at 5pm.
Sports reporter Anthony Joseph revealed the move on X, writing: "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."