In response to Freedom Of Information requests, Staffordshire Police said it had received two reports and West Mercia Police said it had three reports over the past three years. West Midlands Police has also been approached.
The most notable account came from a member of the public in Hartlebury, a village near Kidderminster, who said they saw a line across the sky "the size of six football pitches" at around midnight.
Meanwhile in Dawley, Telford, a member of the public said they saw a bright UFO which looked like a "dinosaur" during the afternoon.
The UK Government shut down its UFO desk, run by the Ministry of Defence, in 2009 - meaning there is no longer an official body that can investigate sightings.
Instead, reports are sometimes made to the police.
Details of logs from West Mercia Police, which covers the Wyre Forest District and Shropshire, reveal that at 00.07am on May 25, 2019, a sighting took place over Hartlebury. A member of the public said: "I think I have seen a UFO. There was a line across the sky the size of six football pitches and then it faded away."
Police revealed whether officers were sent out to each call in the UFO logs. On this occasion they didn't go.
But police did attend a call made from Bromsgrove, in Worcestershire, at 01.05am on April 11 this year, which turned out to be a false alarm.
In the police log, a member of public said: "There is some really strange looking lights in the quarry. I saw lights through the trees and thought that it was a UFO. It was the moon."
The final report made to West Mercia Police came at 3.25pm on July 22, 2019, in Dawley, Telford.
A member of the public reported seeing a "strange UFO-like object" through the curtains. It had "bright white lights and the shadow looked like a dinosaur shape," said the caller. Police did not attend the scene.
Staffordshire Police received a report of a UFO in Burton-on-Trent at 03.21am on January 7, 2018. The caller reported seeing a "UFO in the sky" with a "series of lights on it" while it was stationary.
The other report said a "really bright UFO was in the sky" in Stoke-on-Trent at 04.08am on August 16, 2017.
In one of the two cases, police said "the area was searched" but came back "negative". Police did not specify which case that was.
Stafford was named as a hotspot for UFO sightings following a separate FOI dating back to 2009.