Ben, from Sheffield, was 21 months old when he disappeared on 24 July 1991.
His mother Kerry has always maintained her son, who would now be 26, is alive and was probably abducted.
South Yorkshire Police said officers travelled to Kos on Sunday and would hold a press conference on Tuesday at the site where Ben was last seen.
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Ben vanished after travelling to the island with his mother and grandparents who were renovating a run-down farmhouse building in the village of Iraklis.
Ms Needham said: "We believe someone on Kos does know something - and if they do please come forward. It doesn't matter how insignificant they think it is - if they have information let the police know."
Det Insp Jon Cousins said: "The lives of Ben Needham's family were ripped apart when he disappeared more than 20 years ago and their determination to find him has not diminished.
"They are more desperate than ever to find answers about what happened to him."
He said officers would be "actively" distributing leaflets and posters and carrying out "house-to-house visits" in the Iraklis area.
"It is likely that someone out there knows what happened to him and we will be appealing to people in Kos who have information to come forward and tell us what they know.
"The force is working closely with the Greek authorities to ensure a number of lines of existing enquiry are explored."
He also said there was a "£10,000 Crimestoppers reward available" for anyone who provided information leading to the discovery of Ben.
Earlier this year, the force secured £450,000 from the Home Office to investigate the disappearance of toddler Ben Needham for another six months.
A DNA test was carried out on a man in Cyprus in an attempt to establish if he could be the toddler, but proved negative in 2013.
In 2012, a police operation focused on a mound of earth and rubble close to where Ben was last seen, but no trace of him was found.
A team of 10 police officers has returned to the Greek island of Kos to carry out "house-to-house visits" in the search for missing Ben Needham.