The badly decomposed remains were found on Thursday afternoon in undergrowth close to The Mall, Cribbs Causeway.
Although not yet formally identified, police believe it is him "due to personal items found at the scene".
The 73-year-old went missing in July 2015 and there has been a high-profile campaign to find him.
Mr Serpell-Morris' family has been notified of the latest development.
His nephew, Steve Griffiths, said the person who found his body has done "a great deal to help our family heal".
"I've got pictures [of Derek] all over the wall and I'm constantly thinking of him."
Det Chf Insp Matthew Iddon said: "This is a very distressing time for Derek's family who've been carrying out an exhaustive campaign to locate him and raise awareness of his disappearance and our thoughts are very much with them.
"We're not able to confirm any more details until the post-mortem examination and formal identification procedures have been carried out."
He was last seen leaving the Criterion Pub in St Pauls, Bristol, in the early hours of 11 July 2015 and was reported missing on 23 July.
Avon and Somerset Police say they are "treating the death as unexplained".
DJ Derek, a former accountant, was known to thousands of music fans and played hundreds of sets at local clubs and pubs, as well as at the Glastonbury festival.
He was a resident of St Pauls in Bristol since 1978 and also appeared at gigs across the UK including the Big Chill, worked with Massive Attack and appeared in a Dizzee Rascal video.
There have been a number of tributes to DJ Derek on social media.
Fellow DJ Rob da Bank tweeted he was a  "dj legend, incredible music buff and will be v missed".
Documentary maker Helena Appio made a film about DJ Derek and said he was a "kind and gentle man".
"He was very warm, he was very understanding. He wasn't in any way prejudiced and he felt he very much had this affinity with the black community."
She added: "He was a real British eccentric in the most wonderful way."
In 2012, DJ Derek won the Lord Mayor's medal for his "outstanding" contribution to the music scene in Bristol.
Police "strongly believe" human remains found north of Bristol are those of missing Derek Serpell-Morris, known as DJ Derek.