The Canaries boss is keen to add more firepower to his team, who lost 5-0 to Liverpool at Anfield, and has also enquired about Celtic's Gary Hooper in addition to Graham, who has also been linked with Sunderland.
"Most (people) are aware we have put in a couple of offers for players," said Hughton, who confirmed Graham was the subject of one of those offers.
"That will be down to the powers that be to decide whether there is any mileage in it.
"As a squad numbers-wise we are okay but if there is the opportunity to add quality to add to what we have got then we will look to do that and I've worked hard to do so.
"We have made bids for two players. The other clubs will have the say on whether that goes any further than that."
- Sports & Recreation