The Black and Whites are in the hunt for a stand-off in 2017 and Love Rugby League understands they are interested in Norman.
The Eels playmaker is on a large contract, believed to be worth around £400,000 a year, and is likely to leave the salary-cap strained western Sydney club at the end of the season.
According to reports, Norman is keen to stay with Parramatta but the blue and gold have offered him a three-year deal that is worth less than the current contract he is on.
Norman is demand from a number of NRL clubs after starring for Parramatta this year.
The five-eighth or fullback debuted for Brisbane in 2010 and joined the Eels in 2014. He has made more than 100 appearances in the NRL.