Philip Morrison, 40, denies killing 24-year-old Derek Sheerin, in 1994 in Glasgow.
The High Court in Glasgow heard how he gave a police statement hours after Mr Sheerin's body was found near the Celtic Supporters' club on London Road.
In it he said Mr Sheerin was depressed and had talked of taking his own life and making it look like an accident.
Retired police inspector James Wallace, 51, told prosecutor Iain McSporran QC that he was approached by Mr Morrison hours after Mr Sheerin's half-naked body was found by three schoolgirls in September 1994.
Mr Morrison was then taken to London Road police station where he gave a voluntary witness statement.
He had said Mr Sheerin had been badly affected by the recent death of his uncle Pat and had talked about suicide for five or six minutes.
Mr Morrison said to officers: "He went on like that for five or six minutes.
"I told his mother and sister and they were concerned, but didn't think he would do it."
The court heard that Mr Sheerin and Mr Morrison were staying at Mr Sheerin's sister's house.
Mr Morrison had said: "Derek left the house at 6.30pm and said he was going to his mate's.
"When he left I saw him walking towards London Road. That's the last time I saw him."
It is alleged Mr Morrison compressed Mr Sheerin's neck with a belt and robbed him of a watch, tobacco and Â£20.
The trial before judge Lady Rae continues.
A murder accused has claimed the last time he saw the victim, he was walking off to see a friend.