Alice, 14, from Hanwell, west London, went missing in August and her body was recovered from the River Brent in west London on Tuesday.
Police believe a badly decomposed body found yesterday in dense woodland in Boston Manor Park, west London, is that of Zalkalns.
Scotland Yard said yesterday that although no formal identification had been made “early indications suggest the body may be that of Arnis Zalkalns”.
According to reports, the man was found hanged.
Police stood guard at all entrances to the park last night which stayed closed.
Officers could be seen walking inside the park, particularly under the M4 flyover at the Brentford end of the park, and a forensics van could be seen.
Zalkalns, 41, had been spotted following Alice along a canal towpath. The convicted killer has been missing since September 3.
Alice was last seen on CCTV walking beside the Grand Union Canal near her home on the afternoon of August 28.
Nearly three weeks later investigators realised that Zalkalns, who was reported missing by his family on September 5, had been cycling behind her.
Zalkalns, who had been in the UK since 2007, served seven years in prison in his native country for bludgeoning and stabbing his wife Rudite to death but it is not clear if the UK authorities had any record of his conviction.