Police have this morning revealed that builder Arnis Zalkalns served seven years for murder in Latvia after being convicted in 1998.
Detectives say he was also arrested in London in 2009 for indecently assaulting a 14-year-old girl, but no further action was taken.
The allegation of indecent assault was not pursued because the victim refused to give further evidence. It is reported to have happened in the Ealing area of West London.
Arnis Zalkalns went missing a week after Alice and used the Grand Union Canal route to get to work.
Alice, from Hanwell, was last seen on CCTV cameras on 28 August by the same canal route in west London.
Mr Zalkalns was seen on CCTV on 28 August cycling along Brentford Lock at 4pm, some 15 minutes after Alice walked that route. He was last seen on 3 September.
Detectives believe he is likely to have come across Alice as they were both going in the same direction, north along the canal towpath.
Det Supt Carl Mehta is quoted as saying that his understanding is that the UK had no record of Zalkalns' conviction.
Zalkalns has not used his bank accounts or mobile phone since September 3 and his passport was left at home. The Latvian has been in the country since 2007 and could potentially pose a risk to the public.
Police have received more than 100 phone calls from the public since the Crimewatch programme aired on Tuesday night in which DCI Andy Chalmers was interviewed about Alice Gross and Arnis Zalkalns by presenter Kirsty Young.
Arnis Zalkalns became a 'person of interest' to police on September 12 and could still be in the UK.
Detectives are still not treating the disappearance of Alice Gross as a murder inquiry because there is no evidence that Alice Gross is not still alive.