The 28-year-old has been an integral part of Gordon Strachan's championship winning sides since his £600,000 move from Wolves in 2006.
Hull City boss Phil Brown would welcome a player with Champions League experience as he seeks to ensure his side's survival. A fee of £2 million was suggested by the paper.
He said: "I saw the talk about Naylor, but he's not one I'm really pushing for at the moment.
"He's a decent player and I've looked at him before. But I think that is more his agent putting that one around than anything."