The England Under-21s star has been linked with several top-flight clubs and, while the chairman confirms that they have asked to be "kept in the loop", the Swans have made no bid
The 21-year-old has attracted interest from several Premier League clubs for many months, following a series of impressive performances for the Championship club, and almost joined Cardiff City in the summer.
Ince has scored seven goals in 21 matches this term and reports claimed that Michael Laudrup's side had contacted the Tangerines with an offer, which Jenkins denies.
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"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 says that 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."