The Scottish Premiership leaders have the opportunity to move seven points clear at the top of the table.
The 23-year-old had to be replaced by Nir Bitton during the Hoops' victory over Hearts on Saturday due to a concussion and The Scottish Sun reports that after sitting out training, it is unlikely that he will play any part against Paul Hartley's men.
The news that the Australian is likely to miss the clash at Dens Park is a slight blow to the club's chances of extending their lead at the top of the Scottish Premiership to seven points.
Rogic has been one of the most productive players in the Bhoys' squad this term, scoring seven goals and contributing six assists in the top flight.
And it was his hard work that put Celtic in front during their weekend win as he managed to win the ball back from the Hearts defender before sliding an excellently-weighted pass into the path of Patrick Roberts, who proceeded to lift the ball over the goalkeeper to turn the game on its head following the away side's opener.
But while Rogic has been impressive this term, Ronny Deila has a large group of attacking-minded midfielders to choose from, so the manager is probably thinking that it makes more sense to give him a chance to recover fully.