The 26-year-old has been linked to a number of clubs following the Jack and Army's relegation from the Premier League, with reports suggesting that Fulham’s initial £8 million bid was rejected this week.
"There was no iota of truth in the story that Celtic were closing in on Jordan. No iota of truth or whatsoever," Tackie told Goal.
"Of course there are clubs knocking on his doors [ahead of next season] but I cannot confirm, conclude or say anything about it as at now.
"On Fulham, according to Sky Sports, they've made an £8 million offer to Swansea City but I haven't been told of any rejection. I heard about their offer in the news and read it also on social media but I can't confirm or deny [that Jordan is aware of the impending deal].
"If you were Jordan, between Premier League and Championship, which one would you choose?" he quizzed.
Tackie also revealed that there will soon be an announcement for Jordan's elder brother Andre, who rejoined Swansea from West Ham United during the January transfer window.
"With Andre, I'm sure that in few days to come, you will get to know where he will be leaving to [for the new season]," said Tackie.
Goal understands that Fulham will submit an improved offer next week to Swansea and the deal could be concluded before the World Cup ends.