The 21-year-old has attracted interest from several Premier League clubs in the past following a series of impressive performances for the Championship outfit, and almost joined Cardiff City in the close-season.
Ince has scored seven goals in 21 matches this term, and rumours have been rife that that Michael Laudrup's men have been in contact with Blackpool over a potential deal.
However, Jenkins confirmed that while he had asked that Swansea be kept up to date regarding the England Under 21 international's availability, a bid has not been placed.
Speaking to The South Wales Evening Post, he said: "I am not in discussions with Blackpool. We keep our hand in and we check what's going on with certain players.
"We've asked Blackpool to keep us in the loop on Tom Ince, and that is as far as it has gone. That's just us doing our job."
Swansea have also been linked with a loan deal for Liverpool forward Iago Aspas, but Jenkins said the club are waiting to discover the extent of injuries within their squad before making moves in the transfer market.
He added: "This is the quietest start to a transfer window I can remember. At this point I am not sure what we are going to do.
"We are waiting for players to come back from injury and we'll have to see"
One player who will not be joining the club, though, is Everton centre-back John Heitinga, with Jenkins adding: "That has never, ever been discussed."
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