The 21-year-old medical student, from Bishopbriggs, East Dunbartonshire, disappeared from the city's Renfield Street last Wednesday afternoon and has not been in touch with his family since.
Officers have discovered that Manvir boarded a bus at Buchanan Bus station shortly before 11pm on Thursday.
There is another confirmed sighting of Manvir getting off a bus in Manchester shortly before 4am on Friday.
Investigations are continuing into whether he travelled further. It is understood that there are unconfirmed CCTV sightings of Manvir in London.
On Saturday the Evening Times told how his family were desperate for him to get in touch.
His dad Harpal Singh has now issued a direct plea to his son.
He said: "Manvir, please get in touch with your family, or the police or a buddy, just to let us know you are safe. We don't mind if you want to stay away, we just want to know you are okay."
The 50-year-old, his wife Kirandeep, 41, and their 14-year-old daughter Hartneet are becoming increasingly concerned.
They feared his disappearance could be connected to exam results.
Mr Singh said: "The longer it goes on the more unbearable it becomes. In the CCTV Manvir didn't look himself. It's so unlike him to do this."
Manvir, a member of local dance group Punjabi No 1, is a third year student at Glasgow University.
A spokesman for the university said: "We would urge anyone who has any information about Manvir Singh to get in touch with us or with the police."
Chief inspector Rob Hay, of Kirkintilloch Police Office, said: "It is almost a week since he was last seen in Glasgow and his family are very distressed."