Carlisle though have already turned down a £250,000 bid from Huddersfield for the 13 goal striker.
And along with Barnsley and Dundee United, the Swans and Preston have been linked with a move for Graham, 23.
Terriers chief executive Nigel Clibbens said: “We’re not going to talk about individual targets and enquiries that we make until the deal is done.
“I’m not going to talk about Danny in particular
He continued: “What I will say is that the club are looking to bring in quality players who are capable of excelling at this level and going onto higher levels.
“Therefore when we’re linked with players such as Danny Graham that’s par for the course.
“We have valuations that we put on all the players that we try to bring into the club and the selling clubs will have their own valuations.
“What we’ve got to do is try to get the best value for the club – we make a fair offer.
“We’ll watch developments and we’ll see how things move through the rest of the period with all the targets the club have got.”
The Swans could be on the look out for a new striker although Nathan Dyer has said he could play in that position
