Jones was Swansea's preferred target to replace Brendan Rodgers in the summer. He'd worked alongside Roberto Martinez at the Liberty Stadium before moving with him to Wigan in the summer of 2009.
Martinez, though, is confident Jones will not move to Burnley, and has issued a hands off warning to Burnley. "It's always a massive compliment when other clubs see the good work that you are doing at your football club," Martinez said.
"That's the case for players and it also applies for the staff as well, in this case Graeme. What we have to do is keep focused on the job we have to do here, and the goals we have set ourselves to achieve this season.
"This is a really important time at our football club, and it could turn out to be a significant building block in our legacy as a football club. We are very focused on what we have to achieve this season, and that's not going to change."
Martinez added: "I'm sure he'll take the rumours on board, but he won't let it affect his work in preparing for Saturday's game. "