The Eagles have been linked with the 21-year-old Frenchman for some time and the Scottish Sun reports the club enquired about the possibility of signing Dembele on Wednesday.
However, Celtic made it clear they had no intention of selling the young forward and as such no official bid was lodged by Palace.
The Premier League club could be tempted to move for Dembele in the summer however, and Celtic may be willing to listen to offers as they will have time to line up a replacement – something they would have been unable to do in the closing stages of the January transfer window.
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.
Southend manager Chris Powell led the applause for Jason Demetriou after the right-back scored twice in the 3-1 win against Portsmouth at Roots Hall.
Morecambe boss Jim Bentley was the happier manager after Gregg Wylde's 90th-minute strike earned his side a point in their 1-1 draw with Forest Green.
Manager Gareth Ainsworth described Wycombe's 2-0 win at Cheltenham as a thoroughly professional performance.
Skipper Richard Wood scored the winner just before half time as in-form Rotherham pulled off a 1-0 victory at League One leaders Shrewsbury.