The bid is believed to be in the region of £5 million but, if the player's agent is to be believed, the 20 year-old's club has rebuffed the approach.
Ohore is attracting a lot of interest from across Europe following some fine displays with Nordsjaelland in the Champions League, with Manchester United and Newcastle United being credited with an interest.
With Fulham setting their stall out early, though, Martin Jol is quite clearly eager to strengthen his back-line and he is expected to return with a better offer after the initial rebuke.
Speaking to Expressen.de, Okore's representative, Nikola Juric, seemed to confirm the rumours of a Fulham bid.
"I heard that Fulham made an offer to sign Okore but his club rejected the proposal," Juric said.
"A lot of teams are interested in him. Half of the clubs in the Premier League are after him, so is Lyon and many others.
"He is only 20 years old and, if he signs with a club in England, he obviously won't be expecting to be playing regularly right away.
"So he knows that he has to be thorough, sorting through all these offers and, for him, the most important thing is that a new club has a plan for him."