Celtic, Real Sociedad, Reading and Wigan Athletic are all today reported as being also interested in the Spaniard as their next manager.
Speaking to Setanta Sports, Jenkins said: "The situation hasn't changed. "We've just received a tentative call enquiring about Roberto and obviously, as things stand, he's our manager, he's got a contract with us and he's here for the next few years, I hope.
"I've spoken to Roberto over the weekend. "He's fully aware of any enquiries we get, which is how we deal with things. He's away for a few days now and he's obviously going to have a think and see how he feels.
"We've never talked through about staying or going. I think he's got to think about where he is in career development.
"Quite naturally we want him to stay with us and to take Swansea City forwards over the next few years.
"We've got a little bit of money available to strengthen the squad and make sure we start a little stronger than we finished and hopefully we can look forward to a good season next year."
If Martinez were to be tempted away from South Wales and many City supporters will hope that he isn't, many Swansea fans would like Swansea born Coventry City boss Chris Coleman as their new manager and rumours still abound that The Swans could look in City's direction if they needed a new boss.