Graham has been in and out of the Swans side this season due to injury and the form of summer signing Michu but could become a key player in Reading’s attempt to stay up.
The former Middlesbrough and Watford striker was an instant success in the Premier League last season under Brendan Rodgers, notching 14 times to be the South Wales club’s top goalscorer.
Reading’s need for goals is clear to see as summer signing Pavel Pogrebnyak has been unable to find his shooting boots, while Jason Roberts, Adam Le Fondre and Noel Hunt have fared no better.
McDermott knows Graham from his time at Carlisle but despite admitting an interest in signing a striker, the Reading boss has not yet made an offer the English forward.
“He’s Swansea’s player and I think there is a bit of interest in him,” McDermott told Goal.com
“He’s scored a couple of goals lately in the league.
“I’ve known Danny since he was at Carlisle. He’s another who has developed over time.”