Jenkins admitted on Monday morning that Scottish side Celtic had been refused permission to speak to the 35-year-old but would wait to see what Martinez wanted to do upon his return from holiday before completely turning down their request.
But Martinez, who has seen his stock rise dramatically since taking over at the Liberty Stadium two years ago, has also been heavily linked with a move to former club Wigan if, as expected, Steve Bruce leaves them to join Sunderland.
Asked if he had taken a call from Wigan chairman Dave Whelan, Jenkins told BBC Sport Wales: "I'd probably be surprised if I didn't have one but again we'll have to see what happens over the next few days. We'll do everything in our power to keep him (Martinez) but ultimately it always comes down to the individual himself, how he feels and what he wants to do with the next step of his career really."
Jenkins has also spoken to Sociedad about Martinez, with the Spanish side keen to appoint him as their manager.
"We have had a few brief calls, nothing more than that, which is quite natural with the season we've had and the publicity he's had he's probably quite high on a number of peoples lists which is good in one respect but obviously it can also bad in some other ways," he added.