The club's assistant manager Ally McCoist is reported to have called for the overhaul after a weekend match that saw players sliding across the Glasgow pitch.
This follows news that Steve Welch, head groundsman at Wembley, has lost his job at the London pitch, which is to be returfed.
Hampden Park spent around £120,000 replacing the turf in March after complaints about the quality of the surface.
Hampden Park director David Kells said: "Some of the claims that the pitch was like a ploughed field were wide of the mark. It was watered before the game, which was not we would have recommended.
"But what we have for this time of year is a very good, lush pitch. We won't be sacking the head groundsman. Stephen Bache is first class and his team care passionately about the pitch."