The 30-year-old has been missing from his home in Maryhill since February 14.
Officers were at the Ben Nevis Bar in Argyle Street and the Gala Casino in Sauchiehall Street, recreating Ross's last known movements.
Chief Inspector Ann Hughes, said: "We know that Ross entered the Gala Casino early on Friday, February 15, just after midnight, and what's unusual about that is he walked in, handed over his wallet and mobile phone to the receptionist and left.
"We have absolutely no idea why he would do that. It's a particularly strange set of circumstances."
She said officers are keen to speak to three people who were in the area at the time when Ross was last seen.
She said: "Part of our enquiry has involved an extensive review of CCTV in the city centre.
"Part of that footage shows three people who crossed Newton Street between midnight and half past midnight, and that is round about the time that Ross would have been in the area.
"I'd appeal that if you were one of those people please come forward, because you might just have seen Ross, and it could be the piece of the jigsaw that we need to reunite him with his family."
As revealed in later editions of yesterday's Evening Times, Ross's family made an emotional appeal for information to help trace him.
Mum Sandra, 56, said: "We are terribly worried about him and desperate to find out if he's OK and safe.
"To anyone that has any information about Ross whatsoever we urge you to contact the police.
"Ross we love you very much and miss you dearly.
"Your family and friends want you home."
Ross's brother, Ryan 19, added: "Ross you know we will always be here to help and support you and we love you and miss you."
Ross was last seen leaving the Gala Casino in Sauchiehall Street.
He is 6ft tall and slim with auburn, shoulder-length, straight hair.
When he was last seen Ross was wearing a grey, bomber jacket with black lining and a hood, light blue bleached jeans which were ripped at the bottom and grey hi-top trainers.
Anyone with information is asked to contact Maryhill Police Office on 0141 532 3700.