The Premier League trio are all keen on the Swedish international, who is set to be available for free when his contract expires in January.
Despite adding to his wide options over the summer by signing Nathan Redmond, Canaries chief Chris Hughton is still keen to draft in Hamad.
He sees the Azerbaijan-born ace as the ideal man to inject further pace and creativity into his side and get the best out of star striker Ricky van Wolfswinkel.
Malmo are keen to keep their captain, but are beginning to come to terms with the fact that it may be difficult to convince him to reject a move to one of Europe’s top leagues.
The 22-year-old is wanted by a host of clubs across the continent, with Serie A outfit Genoa thought to be particularly keen.
Fulham and West Ham are believed to be in the race, but Norwich are more willing to offer him first-team football, which is believed to be enough to tilt the odds in their favour.
Could Jiloan Hamad be a hit at Carrow Road?
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