Morrison is currently working with Carlton chief executive Gerry Murphy to recruit a chief executive for the ITV network, following the resignation of Stuart Prebble when ITV Digital collapsed.
Reports over the weekend suggest that once a replacement for Prebble has been found, Morrison will step down.
Granada chairman Charles Allen is also thought to be coming under pressure from shareholders to quit over his part in the fall of ITV Digital and ITV's subsequent loss of the UK digital terrestrial franchise to a BBC/BSkyB venture.
Shareholders are said to have lost confidence in Allen because of the vast amount of money the companies invested in ITV Digital. The broadcaster's losses are understood to have amounted to more than £1bn, as opposed to the £800m it had been originally believed to have lost.
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