Jenkins is unhappy at how long the deal has dragged on leaving Swansea with little time to bring in a replacement for Sinclair at the Liberty Stadium.
"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," noted Jenkins.
Jenkins is also hopeful of bringing in a couple of new faces before the transfer window slams shut on Friday.
"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," added Jenkins.
"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."