Graham has fallen out of favour at the Liberty Stadium this campaign and has admitted he is frustrated with time on the sidelines and is planning talks with manager Michael Laudrup.
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"He's Swansea's player and I think there is a bit of interest in him," he told The Sun.
"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."
Reading have already confirmed the capture of Daniel Caricco from Sporting Lisbon, who trained for the first time with his team-mates on Thursday.
McDermott has also commented on the club's ongoing attempts to sign midfielder Tomas Rogic from Central Coast Mariners.
The 51-year-old continued: "It's not done yet - far from it. We have to speak to Tom and we will see. If we agree then we have to get a work permit.
"We felt he was a good prospect a year ago and it's the same now. He was here for two or three weeks this time last year and we got turned down on a work permit. If it goes that far again then hopefully we can get him in.
"There's good video coverage of him now and people at an appeal would be able to see that.
"He hasn't actually been playing football for that long. It's a bit like Shane Long - he didn't play until he was 14 and had been playing Gaelic football and Hurling."