The Sun says Reid had to physically restrain Wigan boss Cook at half-time of the League One side's FA Cup shock.
Both sets of coaching staff were arguing on the touchline, with Pep and Cook squaring up.
As the whistle went for half-time, the bust-up continued in the tunnel as Pep put his hands on Cook while the duo continued to bicker.
And as Cook began to bark back at Pep as he walked towards the home dressing room, Reid stepped in to drag the Latics boss away.
Reid, who has worked as a Latics coach on a voluntary basis this season, was heading pitchside in his role as a pundit.