Milosevic is regarded as one of the best young defenders in Europe after impressing for club and country over the last 18 months.
The likes of Liverpool, Arsenal, Spurs, Celtic and Fiorentina have all been credited with an interest in Milosevic in the past and now Fulham are keeping tabs on the centre-back.
Fulham boss Martin Jol is thought to be keen to bring in a central defender and the Craven Cottage outfit are expected to have Milosevic watched in midweek when Sweden's Under-21s take on Poland as they continue to monitor his progress.
AC Milan and Eintracht Frankfurt are also thought be keen on Milosevic and have watched him on several occasions this season.
The 21-year-old is entering the final year of his contract at AIK and the Swedish club are bracing themselves for offers for Milosevic.