Indian federal police filed charges against more than 25 people in May including Modi, Choksi, former PNB chief Usha Ananthasubramanian, two of the bank's executive directors and three companies belonging to Nirav Modi.
Meanwhile, Hindustan Times reported that a letter rogatory had been sent to British authorities by the CBI and Enforcement Directorate, seeking investigation and information on Modi, who arrived in the United Kingdom before his Indian passport was revoked in February.
London-based newspaper Financial Times on Sunday reported that Modi was in London trying to claim asylum from what he called "political persecution".
The confirmation that Nirav Modi is in the United Kingdom comes hours after global business daily Financial Times, citing Indian and British governments, reported that the billionaire jeweller is in London where he is trying to claim asylum from what he calls "political persecution".
Stars such as Kate Winslet, Rosie Huntington-Whiteley and Naomi Watts, have been seen wearing his products.
Once, an RCN is issued, member countries of the Lyon-based worldwide police cooperation agency can arrest and extradite Modi, who fled the country in the first week of January, weeks before the bank filed a complaint with the CBI.
Britain's Home Office said it does not provide information on individual cases, while Modi could not be contacted by Reuters for comment.
But he fled India in February for an unknown location after being accused of being at the centre of a $1.8-billion fraud involving India's second largest public lender, Punjab National Bank (PNB).
Modi, the third generation of his family to go into the diamond trade, is worth $1.73 billion according to Forbes, placing him 85th on India's rich list.
The Enforcement Directorate, India's financial fraud-investigating agency, had unsuccessfully approached Interpol in March for an worldwide arrest warrant.
Last month, External Affairs Minister Sushma Swaraj had said Prime Minister Narendra Modi had conveyed his unhappiness to his British counterpart Theresa May over focus on conditions of Indian prisons during court hearings on Mallya's extradition. The case has soured British-Indian relations.
India's PTI news agency quoted unnamed sources as saying that Williams confirmed in the meeting Modi's presence in Britain but that she had promised London's full cooperation.