Alan Shone, 61, was last seen almost a month ago (Monday 22 August 2016) at his home on The Crescent, Irlam.
It is thought he caught the 67 bus from Irlam to Eccles to collect a prescription from his doctors.
He got off the bus at the Patricroft Bridge stop at the junction of Aldred Street, but never returned home.
Police have received reports of two potential sightings of Alan on Monday 22 August.
The first was at 11.30am on Princes Avenue at the junction with Liverpool Road, Irlam.
The second was between 12.40pm and 1pm near to City Airport, Barton-upon-Irwell on the A57 heading towards Irlam on foot.
Alan is white and around 6ft 2in tall, of a medium build with greying hair, which is thinning on top. He also has a moustache and green/blue eyes.
On the day he went missing, he was wearing a grey and white collared t-shirt, a grey fleece with large pockets at the front, dark blue jeans and a black belt.
The brown shoes he was wearing have light coloured soles and he is likely to have been wearing a blue denim baseball cap.
He was also wearing a gold ring with the word ‘MUM’ on it, a silver wedding ring and a silver chain with a St Christopher medallion.
Police are urging Alan or anyone who knows where Alan is or may have seen him to get in contact.
Detective Sergeant Tim Flint of GMP’s Salford borough, said: “Alan, please make contact with us to let us know that you are safe and well.
“Your family are worried about you and just want you to return home.
“I’d also like to ask anyone who knows where Alan is or has seen him to get in touch with police as soon as possible.”
Anyone with information about Alan’s whereabouts should contact police on 101 quoting reference number 1669 of 23/08/16