Gordon Wilson, from Leaden Roding, was last seen by neighbours at about 11am on Sunday, October 25.
The 82-year-old is a former headteacher at Shawlands Academy and grew up in the city.
He has vascular dementia and has difficulty speaking.
Wilson would routinely have Sunday lunch with his daughter, Lesley Rankin, who reported him missing after he failed to arrive at her house at the weekend.
The pensioner is understood to have left home on foot with a small amount of cash and some medication. He was last seen at Chelmsford bus station at 12.52pm.
Daughter Gillian Wilson said: “We think there is a high possibility he is trying to go to Glasgow.
“He moved from Scotland to Essex 11 years ago, and spent 71 years in Glasgow, where he was former headmaster at Shawlands Academy — so he knows the city well.
“Many of his former pupils are tweeting and sharing posts on Facebook as part of the appeal to find him, and we are touched by everyone’s concern and assistance.”
Mr Wilson is 5ft11, of medium build with thinning grey hair. He wears glasses and was last seen wearing a sports jacket, either checked or navy. He usually wears a shirt, tie and jumper.
Anyone with information is asked to contact Chelmsford police on 101.