The Barclays Premier League club had been in talks since the autumn with US billionaire John Jay Moores, the former owner of the San Diego Padres baseball franchise, over investment.
But on Friday evening, ahead of a Swansea City Supporters Trust meeting to discuss the issue, a club spokesman said a deal was "extremely unlikely"
And Jenkins, in his programme notes ahead of Saturday's league game with Manchester United, said: "I'm positive that any movement away from the current set-up will only be put in place if everyone connected to our club is convinced it's a good thing for the football club first and foremost.
"If not, and this is my opinion, I can see the status quo continuing for some years to come."
The Supporters Trust, which owns 21 per cent of the club, has welcomed the news that a proposed £30million deal to buy a 30 per cent stake in Swansea, will not go ahead.
But Trust chairman Phil Sumbler, who said the sale of shares would have opened the way for more than 60 per cent of the club to be sold off, told BBC Wales: "If the deal is dead then clearly it was never meant to be, so that's clearly good news to us.
"But now that the club has shown that it is open to potential new purchasers coming in, I don't believe these will be the last people to show an interest."
Source : PA
Source: PA