Roderick Macdonald, 76, was reportedly living in the Algarve region of Portugal at the time of Madeleine's disappearance in 2007, aged 3.
Police have now confirmed he is the subject of active arrest warrants in New Zealand related to four child indecency offences alleged to have taken place in 2009.
He was known in New Zealand as Roderick Robinson, police said. He changed his name to Macdonald after being convicted of child sex offences in the UK, British newspaper The Telegraph said.
London's Metropolitan police want to speak to him about a possible paedophile ring which could have been operating in the area, the paper reported.
He was caught in Malta this week after four years on the run following a conviction for abusing two girls in Brighton, UK.
New Zealand police this afternoon released a statement saying Macdonald was "the subject of active warrants to arrest".
"Those warrants were issued by the Hamilton and Auckland District Courts and relate to four child indecency charges and one passport act charge," a spokesman said.
"In 2009 Robinson absconded overseas while on bail."
Police have been in contact with their counterparts in the UK in recent weeks, the spokesman said.
"As he is now subject of judicial proceedings, New Zealand police will not be commenting further on the matter at this time and refer all enquiries to the UK police."Macdonald was reportedly deported from Portugal to Australia in 2010 to face charges of raping an 8-year-old girl in 1989.
While on bail the British man fled to New Zealand.
Radio New Zealand reported he was arrested while in New Zealand for child sex offences.
He was granted bail on the basis that he surrender his passport but then used a stolen passport to leave the country and fly to Portugal.
An international arrest warrant meant he was arrested in a campsite in the Algarve in 2010, The Telegraph reported.
Macdonald served a six-month sentence in Australia for indecent assault.
He later moved to Brighton, where in June 2012 he was accused of abusing two sisters, aged 5 and 7. He was convicted, but fled the UK before he was sentenced.
He is wanted in the UK for absconding, and for failing to notify authorities he had changed his name from Robinson to Macdonald, changed his address and was going abroad.
An extradition order was made by magistrates in a court in Malta this week, and he was remanded in custody to be returned to the UK and resentenced.
"We are glad to learn of his arrest, which has come about as the result of close co-operation between ourselves, the Crown Prosecution Service, the Child Exploitation On-Line Protection Centre (CEOP) at the National Crime Agency, and overseas law enforcement agencies," Detective Chief Inspector Carwyn Hughes of Sussex Police told the newspaper.
Now Scotland Yard detectives, who have been re-investigating the missing girl's case, want to question him about paedophile rings in the Praia da Luz area where Madeleine went missing.
They are reportedly looking into 18 possible linked break-ins at Algarve villas by a lone intruder from 2004 to 2010, The Telegraph said.
Madeleine disappeared from her family's holiday apartment in Praia da Luz while her parents Kate and Gerry McCann were dining out with friends at a near-by restaurant.
It sparked a world-wide search for the child, and made global headlines.
She has yet to be found.
By Patrice Dougan of APNZ
