A witness went to police saying that two elderly men had been seen arguing in the woodland shortly before Mr Wrighton was killed, the Daily Mail reported.
Mr Wrighton, from Banham, was found dead last Saturday morning in the woods near East Harling, prompting a huge police investigation.
But a Home Office post-mortem examination later found the grandfather had been stabbed multiple times in the head and neck.
Elizabeth Truss said: "I am deeply shocked and saddened by reports of the death of local man in woodland near East Harling".
His vehicle, a red Skoda Fabia, was parked close to The Street, the road close to the heathland where he was walking his dogs Dylan and Gemma. He then drove his red Skoda 4.5 miles to The Street, close to the area where he walked his dogs.
Cops probing his murder have released CCTV footage of him at Kenninghall Post Office, Norfolk, between 10.08am and 10.12am on Saturday - half an hour before his body was discovered.
On Friday, police said they had traced one of three "vital" potential witnesses - a man in his 50s seen changing into a T-shirt - but they said they still wanted to speak to two other men. This was a particularly brutal murder and to do this, we need to piece together Peter's final movements to understand what happened to him and why.
Detective Superintendent Andy Smith said: "This is a complex investigation and we are pursuing many leads".
The force has said anyone with information should contact them immediately. It is believed he was wearing a grey or blue t-shirt and grey floppy gym style shorts above the knee and heavy duty flip flops.
He added search teams were using metal detectors and dogs to hunt for clues, and that more than 100 officers were working on the case.
Anyone with any information should call The Operation Graduate helplines on 0800 056 0944 or 0207 158 0010.
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