As revealed by Goal.com, the Team GB Olympic star is the subject of a £6 million bid from the Premier League champions but the Swans supremo feels that Roberto Mancini's side are being sluggish in pushing the move through.
He observed to the press: "It has been dragging on a while and I'd have thought if they really wanted to sign Scott they would have dealt with it a bit better than they have, but that's their business."
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Jenkins asserted, however, that Sinclair's anticipated departure is not the deal on which Swansea's remaining transfer business all hinges, with manager Michael Laudrup hoping to balance his squad before Friday's deadline.
"Hopefully, over the next few days, we'll get a couple more signings in and we can put the transfer window behind us at the end of the month," the chairman continued.
"Our proposed signing of a couple of players is not dependent on Scott's transfer out. I think it's more about numbers and making sure we have the right number in the squad."