Garry Kane, 41, who struggled with heroin addiction, denies murdering Kathleen Milward, 87, on January 3 this year.
The High Court at Dumbarton heard that traces of Mrs Milward's blood were found on Kane's boots, on the front and back of his jeans, and in small amounts inside the pockets.
Under questioning from advocate depute Jennifer Bain, the forensic scientist Dr Nighean Stevenson said Kane's DNA was also found on the pensioner's head, neck and hands as well as on a handbag and purse in her bedroom of the property in Stonehouse, South Lanarkshire.
Dr Stevenson, 40, said the blood on Kane's clothes could have been there as result of him assaulting his grandmother.
She said: "The scientific findings would support the assertion that blood from Kathleen Milward had been deposited by contact and by aerial transfer on the jeans and deposited by contact on the toe area of both Hi-Tech boots.
"If Garry Kane had worn these jeans during an assault on Kathleen Milward while she was bleeding, this could be an explanation for our findings."
However, Dr Stevenson added that she "could not rule out the possibility that it could have been transferred on to his jeans while attempts at resuscitation were carried out while she was bleeding".
Moreover, no traces of blood were apparently found on Kane's aunt, Maureen Kennedy, 58, who had administered CPR to Mrs Milward.
It is alleged Kane repeatedly punched and kicked Mrs Milward, struck her on the head and body with a blunt implement, placed his hand over her mouth, applied pressure to her neck, and murdered her.
The trial, before Lord Matthews, continues.