The 20-year-old Danish international defender has been heavily linked with a move to England, following a number of impressive performances for current club, Nordsjaelland, particularly in the Champions League this season.
Red Devils boss Sir Alex Ferguson is rumoured to be interested in bringing Okore to Old Trafford, despite the wealth of central defensive options he currently has to choose from.
Newcastle United are another club monitoring the young centre-back's situation, but according to Okore's representative, Nikola Juric, it's Fulham boss Martin Jol who has made a firm offer for the player's signature.
"I heard that Fulham made an offer to sign Okore but his club rejected the proposal," Juric told Expressen.se. "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."
Interest in Okore extends further afield than England, with Ukrainian duo Dinamo Kiev and Shakhtar Donetsk both having been previously linked, while clubs in Germany and Russia are also following his progress.