Kent Police said they believe the man in a newly released image is of “crucial importance” to the investigation into the murder of PCSO Julia James.
Assistant Chief Constable Tom Richards said the unknown identity of the man was “a big frustration to the investigation” but did not confirm that he was a suspect.
The popular community support officer was found dead in Akholt Wood near her home in Snowdown, Kent, on Tuesday April 27.
A post-mortem examination revealed she died from significant head injuries.
On Friday, the force released an image of a man who is understood to have been in the Aylesham area the day after, on Wednesday April 28.
The photo was taken on Spinney Lane, close by to where Ms James’ body was found.
At a briefing in Folkestone on Friday afternoon, Mr Richards told reporters: “I’m not saying here and now that he is a suspect, but he is of crucial importance to the investigation.
“We’ve got a large team investigation working on this, we’ve got many names that are featured in the inquiry.
“We are of course interested in many individuals but this individual is a big frustration to the investigation because we don’t know who they are, and we desperately need a name so we can identify them.”
He added that police have yet to establish a motive for the 53-year-old’s murder.
The force said on Thursday that it was broadening the search area to include “a number of other locations” in addition to the woodland where she was found.
Crimestoppers are offering a reward of up to £10,000 for anonymous information that leads to her killer being convicted.
Mr Richards also urged the public to get in touch if they have information.
He said: “Anybody who knows who that man is, we desperately need you to make contact with us and identify who that man is.
“If this person is watching, please contact us, you have crucial information.”
Mr Richards said that any calls to provide information would be handled with “the utmost confidence and sensitivity”.
Ms James, described as “fiercely loyal” by her family, died from serious head injuries while out walking her dog.
On Wednesday, police issued an image of the PCSO in the clothes she was wearing before she was killed.
The picture shows Ms James walking her Jack Russell, Toby, while wearing a light blue waterproof coat, blue jeans and dark Wellington-style brown boots.
Police said it was the same clothing, apart from the gloves, which she wore on the day she died.