Forensic specialists are continuing with their examinations of the foot, which was found on a path near the old railway track in Louth Road, New Waltham, on April 25.
Humberside Police said detectives are also examining local, regional and national reports of missing people.
Extensive searches have been carried out in the area following the discovery.
Detective Chief Inspector Al Curtis said: "Initial indications are that it is a woman over the age of 16, who is around 160cm tall – which is approximately 5ft 2in. However, this information is from preliminary pathological findings and as such we cannot rule anything out at this stage.
“Pathologists have also indicated that the foot is likely to have been deliberately dismembered and that they believe this has happened at some point during the last 12 months.
“Our main focus is to establish who the woman is and how her foot came to be found here.
“We’re examining local, regional and national reports of missing people and while our initial physical searches of the area are now complete we cannot rule out the possibility of further searches being carried out as new evidence and lines of enquiry emerge."
Police are continuing to appeal for anyone with information to get in touch by calling 101 and quoting log 85 of April 25.