Kavanagh, hugely influential for the Owls during a recent loan spell, has been told he can leave Sunderland by manager Roy Keane and Laws has not given up hope of persuading the former Republic of Ireland midfielder to return.
Laws said: "Roy's going to let him go and Graham's currently talking to a couple of clubs as we speak.
"It's looking more and more unlikely that he'll be coming to us because of the wages - that might be a problem.
"But we're still looking to bring him back and looking at having a meeting with the chairman.
"I hope to have an answer by Wednesday."