The Parkhead side's record signing is attracting interest from several clubs across England and Europe.
Nottingham Forest have been keen on the 22-year-old since January and had a £25 million offer rejected.
Other clubs, including Fulham, Crystal Palace, Tottenham, AS Roma, and Atletico Madrid, have also shown interest.
Voetbal Krant has now reported that Forest have submitted their first formal offer of this transfer window for the Belgian.
Roma are also said to be readying a bid, while Villareal have entered the equation.
Celtic manager, Martin O'Neill, admitted there is a level of "resignation" at the club over Engels potentially leaving.
He said: "If, for instance, all those bids that Nottingham Forest made come in on the 11th hour – that was just a non-goer for us at that particular stage.
"So if some things can happen a bit earlier, then maybe there's some resignation on my part."
Engels could move on next week.
O'Neill admitted the club struggle to compete financially.