Nottingham Forests pushed hard to prise the Belgium midfielder away from Celtic over the final days of the winter market.
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The Daily Mail says Forest had opening offers of £14m and £17m rejected over the weekend.
Then on Monday, they returned for a third and final time, offering Celtic £20m up front with a further £5m in add-ons for the 22-year-old.
But the Hoops refused to do business, having signed Engels 18 months ago from Club Brugge for £11m.
It's suggested Celtic would've been more maleable if given more time to find a replacement. While Engels is disappointed, Celtic management expect the midfielder to remain fully committed for the remainder of the season.