The Standing Figure was taken from Glenkiln Sculpture Park on Lincluden Estate, Dumfries and Galloway last week.
Detectives said a group of men in a Ford Transit-style van were previously seen looking at the bronze, worth £3 million.
The three men are thought to be in their 20s or 30s, of average height and build and were accompanied by a collie-type dog.
One of the men had ginger, shaven hair and was wearing a red or orange waterproof jacket.
The van they were in was an "unusual" shade of blue.
Detective Inspector Colin Burnie, who is leading the investigation, said: "We are delighted with the response from the public so far in this investigation, which has helped us immensely. We now require further help to identify this blue van and occupants and would again ask the public to call us if they have any information which may help us."
The 7ft statue, from 1950, was removed from its rock plinth and taken from the park sometime between 3pm on Thursday and 3pm on Friday.
Police said it is not clear whether thieves targeted the bronze for its art value or simply for its scrap metal value.
Several other works by Yorkshire-born Moore (1898 -1986) have been stolen from display in recent years.
Two men were jailed last year for taking a sculpture from the grounds of the Henry Moore Foundation in Much Hadham, Hertfordshire.
Moore's £45,000 painting Three Reclining Figures On Pedestals was one of three artworks stolen from a gallery in Broadway, Worcestershire in 2010.
The Henry Moore Foundation also had to carry out a security review following the theft of a two-ton piece called Reclining Figure in December 2005.