Late on Tuesday the Latics made an official approach to speak to Martinez, who returns from a short holiday on Wednesday, as they prepare for Steve Bruce's departure to Sunderland.
However, they were stunned by the £2million-plus compensation being demanded to release the Swans boss, who only signed a five-year contract last year before guiding the club to eighth place in the Championship.
That sum is considered far too high for a manager who has shown a lot of potential and won many plaudits for the work he has done at Swansea but has no Premier League experience.
But Jenkins is determined to get the best possible price for his manager if Martinez decides he wants to make the step up to the top flight.
"Wigan asked for permission to speak to Roberto. They asked what compensation we would be looking for and we talked about different figures," he said.
"I told them what I valued Roberto at and they told me what they thought - we were miles apart to say the least.
"I have not given them permission to talk to Roberto."
Martinez, a former Wigan player, has also attracted interest from Celtic, Real Sociedad and Reading, with the deposed Scottish champions making their move for the 35-year-old last week.
The Spaniard has, however, distanced himself from comments attributed to him on Tuesday that claimed he would be interested in a move to Parkhead.
"No quotes from me are true because I have not spoken to the press," Martinez told the Western Mail.
Wigan are now considering their options, with several other names being linked to the pending vacancy.
Peterborough's Darren Ferguson, who won promotion from League One this season, is another manager who would command a compensation fee, although probably not as much as Swansea are asking for.
However, Posh director of football Barry Fry insists the club have had no contact from Wigan and claims Bruce has told him Martinez is the man they want.
"We've only had one enquiry and that was from Reading (which they rejected)," he told BBC Radio Cambridgeshire.
"I'm close to Steve Bruce, he tells me Martinez is going to Wigan and I believe Steve Bruce."