Mr Osman (whose real name is said to be Hamdi Isaac), is being held in Rome while attempts to extradite him continue. Two of his brothers are also being held in custody in Italy.
The denial from the Italian authorities comes despite reports that Mr Osman is negotiating a deal "to start a new life in Italy", in return for giving evidence on the Italian network that helped him flee Britain in the wake of the failed 21 July bomb attacks in London.
Mr Osman was arrested in Rome last Friday, after British, French and Italian police tracked his mobile telephone calls across Europe. He is suspected of the Warren Street bombing.
The semi-official Ansa news agency reported yesterday: "Hamdi will stay in Italy" and security sources quoted by Il Messaggero of Rome said negotiations between Mr Osman and Italian authorities had almost certainly "frozen indefinitely" prospects for extradition.
Mr Osman has been formally charged with terrorism offences in Italy although it remains unclear what effect this, or any negotiations, will have on extradition. Hislawyer, Maria Sonnessa, who visited him again in prison yesterday, has warned that the extradition process could be drawn out, even though it is a test case under the new European arrest warrant supposed to expedite cases within the EU, normally within two months.
Judge Franco Ionta, head of the anti-terrorism pool of magistrates in Rome, said Mr Osman would stay in Italian custody "as long as there are investigative needs linked to the issuing of a precautionary arrest warrant".
The main extradition hearing could be as late as September and even if won by Britain, Mr Osman would have a right to appeal to Italy's supreme court.
Last night, anti-terrorist detectives were questioning a man arrested at a flat linked to Mr Osman. The latest arrest, following raids at two properties in south London, brings the number of people being held in Britain over the failed bombings of 21 July to 16.
Police sources confirmed reports that the raid on the flat in Stockwell, south London, on Monday night was carried out because the address had been given by Mr Osman, despite him living elsewhere. Last Wednesday, police raided a house nearby, where he was living with his wife and three children.
Monday night's raid was followed by similar police operations at another address in Stockwell and at a property in Clapham, where another man was arrested.
Police are still questioning three other suspects for the 21 July attacks: Muktar Said Ibrahim, 27, and Ramzi Mohammed, arrested last Friday, and Yasin Hassan Omar, 24, who was held in Birmingham.
Last night, police released a man arrested after raids in Stockwell on Friday 22 July, the day after the failed suicide bombings.
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