On Tuesday morning News Limited reported that Shaw was the subject of a huge five-year, $4 million pitch from the expansion club.
But Giants football manager Graeme Allan refuted that figure in a statement on the club's website on Tuesday morning.
"The claim that we have made a $4 million offer is a wild exaggeration and simply wrong," Allan said.
"We are certainly very interested in Heath Shaw, a premiership player, and we have had discussions with him and his manager, as have a number of other clubs."
Earlier, on Melbourne radio station 1116 SEN, Shaw's manager Ben Niall also said the Giants' offer was smaller than reported.
"You do get a bit of Chinese whispers at this time of the year," Niall said.
"The basis of GWS' circumstances is that they are in a position where they have to make a compelling offer to people to move them, and he's certainly been made a compelling offer.
"But it's nothing like the sort of dollars that are being talked about."
Shaw, who has played 173 games for the Magpies over nine seasons, is contracted until the end of 2015, but has agreed with the club to seek a trade.
The 27-year-old did not attend Collingwood's best and fairest dinner on Friday night.