Gloucestershire Police said they had found evidence that a body could be buried within The Clean Plate café in Southgate Street, Gloucester, and are linking it to the disappearance of 15-year-old Mary Bastholm.
Mary was reported missing on January 6 1968 and has never been found.
Serial killer West, who died in prison in 1995 aged 53, was previously suspected over her disappearance.
Gloucestershire Police said its Major Crime Investigation Team has deemed that further assessments are required at the cafe in order to determine whether an excavation is necessary, with officers expected to be at the scene for a number of weeks.
Family Liaison Officers have now been put in place to provide support and updates to Mary’s family.
A white tent was erected outside the cafe on Tuesday, with police officers stationed outside the building and a police van parked nearby.
Officers were seen carrying evidence bags out of the cafe at about 2pm on Tuesday.
Assistant Chief Constable Craig Holden said: “This could be a significant development on a case which has gained a lot of public interest over the years.
“On the basis of the information provided to us, we consider this to be new and potentially important evidence in the case of Mary Bastholm, however further detailed assessments will take place over the following few days to determine the extent of excavation needed.
“First and foremost our thoughts are with Mary’s family and we would ask that their privacy is respected at this difficult time.
“This news may understandably alarm those who work near to the premises, as well as those in the wider Gloucester community and beyond.
“The Constabulary has always said any fresh evidence would be reviewed.
“This has happened and a focussed and proportionate investigation will now take place.”
He added: “Due to the potential scale of this there will likely be some disruption to those who work nearby, and I ask for their patience and co-operation during this time.
“We will have local officers in the area and a visible police presence at the location possibly for a number of weeks.
“We would also encourage anyone who is affected by this news to please seek support.”
Along with his wife Rose, West tortured, raped and murdered an unknown number of women over a 20-year period.
Fred West was charged with 12 murders, but committed suicide in a Birmingham prison before his trial.
Rose West was convicted of 10 murders in November 1995 and is serving life.