The 58-year-old was walking along West George Street, heading towards a branch of Allied Irish Bank, at around 1.30pm on Monday when he was attacked.
He passed a parked black BMW, with a man in the driver's seat, and another man leaning in at the window.
The man at the window, who is described as being around 50, attacked the man and tried to steal his backpack, which contained a large sum of money.
The victim's friend, a 43-year-old man, was waiting for him nearby and saw the assault.
He ran to help and pulled the attacker off his friend and in to the middle of the street. The two then started fighting in the road.
While the altercation was taking place, the 58-year-old had managed to make his way into the bank, where staff contacted police.
The suspect ran off down West George Street where he got into the black BMW, which had already left the scene.
The car was last seen heading towards George Square.
Police said the suspect is white, around 5ft 11in, stocky, with cropped grey hair.
He was wearing a brown jacket and dark trousers.
Detective Sergeant Scott Douglas, from the City Centre Robbery Unit, said: "Thankfully neither of the men were injured in this assault and I am appealing for the help of the public to trace the men responsible.
"From inquiries so far we know that there was a white van stopped in front of the two men who were fighting in the roadway and saw what took place. I am appealing for the van driver to come forward as he no doubt will have information which can help us.
"I would also like anyone who was in West George Street around 1.30pm on Monday and saw the altercation take place, or saw a black BMW parked on the street, to contact me."
Anyone with information is asked to call City Centre Police Office on 0141 532 3000.