While Jenkins concedes that things could change before the window shuts, he has again stressed that Britton remains a Swansea player for now.
"I have spoken to Wigan in the past but there has been nothing in the past week," the Swansea chairman told the South Wales Evening Post.
"We have had no bids from Wigan for any of our players so as things stand there is no situation with Leon Britton. He is our player.
"As things stand today, I expect Leon to be here when the window closes, but you never know what might happen.
"I can't say anything different to that at the moment because that's the way it is, but Wigan might ring me or Manchester United might ring me, I don't know."