The Italians are keen on signing the Frenchman - who is surplus to requirements at Stamford Bridge - for the whole of next season.
Malouda joined from Lyon for £13.5 million last summer but struggled to find his best form during last season.
Florent Malouda could be on his way to Roma
Roma are widely reported to be interested in signing one or two more top players in the summer.
One of these is believed to be an attacking winger after the departure of Amantino Mancini to Inter.
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London gets ready for the Diamond Jubilee - in pictures
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EXCLUSIVE: I won't play with Joey Barton, says Adel Taarabt
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Diamond Jubilee: Boat by boat, here is where to watch the Queen's Thames flotilla - VIDEO
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Duchess of Cambridge is pretty in pink at her first Buckingham Palace garden party
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News pictures of the day
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London 2012 Olympics: Raising the bar and the Games haven't even started yet. Price of toasting Team GB is £6 a pint! -
Timebomb ticking in Thames Estuary could put Boris Island plans in jeopardy -
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‘We will form a human barricade to keep missiles off our homes’
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Regent’s Park rapist: Teenage jogger assaulted by stranger in terrifying 7am attack
Why I think doctors are right to strike 
Family pay tribute to the London man who gave his life to save a five-year-old girl from drowning 
Eton schoolboys fly Games flag on Everest 
Horror on the 5.53! Commuter dragged 200 feet after getting hand trapped on train 
Shrimpy's - review 
The O2
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Rock star
Happy anniversary
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Summer party
Diamond Jubilee
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Garden party
First review
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Dog save the Queen
