Graham is said to be on the verge of a loan move to Blackburn, with Sunderland keen to offload the 30-year-old.
The Black Cats are eager to make room for new additions, and Graham could be sacrificed, with Blackburn reportedly hunting the experienced forward.
However, Rovers boss Lambert would not be drawn on the speculation, as he doesn’t want to speak about potential additions until they are confirmed.
“Names are getting bandied about but while it’s probably boring for you to write and listen to, we can’t talk about anybody’s players until they come through the door," he said.
If Graham does join Blackburn he will improve their striking ranks, but there will also be further question marks raised over Jordan Rhodes’ future.
Rhodes has been linked with Sheffield Wednesday, with Blackburn said to be ready to accept offers in excess of £12 million.
Rhodes has been Blackburn’s main scorer ever since he arrived at the club from Huddersfield Town, and Lambert also remained coy on the reports linking his star striker with an exit.
“I haven’t heard anything about Jordan leaving since I’ve been here,” Lambert said.
“As far as I am concerned he is our player and we are delighted with his contribution.
“Until a manager picks up the phone and asks the question then I don’t have a problem but I haven’t had any calls at all.”