Javaid Ali, 48, was stabbed in his shop, Sunshine Grocers, in Paisley, Renfrewshire, on June 15. He died in the town's Royal Alexandra Hospital two weeks later.
Strathclyde Police, which has more than 60 officers working on the inquiry, have already visited 700 homes and taken up to 170 statements from potential witnesses.
Police made a fresh appeal for help to trace Mr Ali's killer on Thursday's edition of Crimewatch, and after the BBC programme was broadcast they said they had received two encouraging leads.
One of the calls was from someone who gave the name of a possible suspect and said he had seen the weapon used. A reward of £50,000 has been offered for information leading to the arrest of the person responsible.
Detective Chief Inspector Duncan Sloan, of Strathclyde Police, said: "We had a call from an anonymous male who named an individual responsible and stated he'd seen a weapon that had been used.
"The first is from a male who says he knows information and was going to attend at Paisley police office. This is really encouraging and I would welcome this, but I would ask him to please call back so we can speak to him.
"Clearly this is important and I would urge that caller to please call back. I'll be sitting waiting for that phone call."
Abbas Ali, 25, one of Mr Ali's three sons, made an emotional appeal for help during the programme. He urged anyone with information to think of the trauma caused to his family and contact the police.
He said: "I really want them to be caught, for the sake of my family, so that we can maybe begin to move on. He was a wonderful father, husband, son and friend. I cannot put into words the suffering this has caused our family.
"They came in and told us that he had been, basically, stabbed in the shop. My mum just broke down there and then.
"I just went to reassure her, to say 'mum, it's going to be okay', but as soon as I opened my mouth, I couldn't help it, I just burst into tears as well. It was probably the most horrific moment I've had in my life."
Mr Ali was taken to intensive care after the attack on Friday, June 15, and underwent surgery that same day. However, speaking earlier this month, his younger brother Sha spoke of the moment four days later when they realised he would not survive the attack.
He said: "They took him to intensive care and said the next 48 hours would be critical. But the consultant came to us the following Tuesday and said basically there was no hope. There was no brain activity.
"We prayed for Javaid over the next few days. But nothing could done."
Police have described the murder as "mindless" and are looking at leads gathered during a stop-and-interview operation a week after the attack.
They are still trying to trace a man who was seen walking from the direction of Sunshine Grocers, on Green Road, at about 3pm on the day Mr Ali was attacked. They are also hoping to speak to a young woman carrying Aldi shopping bags who was walking towards Green Road in the direction of the cycle track.