The 16-year-old was seen on CCTV entering Union Square shopping centre before boarding a 202 Stagecoach Bus at 1.11pm at Aberdeen Bus Station on Saturday November 17.
It is understood that he bought a ticket for Raemoir Road in Banchory, however a passenger told Police they believe Liam got off at Crathes.
Officers have been focusing on three areas of interest; Aberdeen Bus Station, Crathes and Banchory.
Detectives were at Union Square, Aberdeen Bus Station and on board a number of 202 buses on Saturday and spoke to several drivers and passengers.
Specialist searches are ongoing in the Crathes area and have included farmland, woodland and some areas of water.
Police have been assisted by the Aberdeen and Braemar Mountain Rescue Teams, whilst specialist resources have also been deployed including a dog unit, road policing patrols and a dash cam appeal at Crathes.
Huge matrix boards are also on display at the entrance to Banchory asking members of the public if they have seen Liam.
Chief Inspector Martin Mackay said: “We are very grateful for the many messages of support for both Liam’s family and the police inquiry and the suggestions we have received.
“All information passed to us will be followed up.
“We don’t know where Liam was intending on going last Saturday and the Crathes and Banchory areas are vast and include challenging terrain.
“Despite searches already carried out Liam is still missing and we are continuing to urge anyone with information to contact police on 101 using reference number 1302 of 18 November.”