The body of a 32-year-old from Burnley was discovered at the landfill site on Whinney Hill Road, Altham West, on Monday.
Workers spotted the body in a consignment of waste following a delivery shortley before 9am on Monday.
It is thought that Mr Marren's body may have travelled from Widow Hill Road in Burnley, another waste disposal site which is being examined.
Further tests will be carried out after a post mortem was inconclusive.
Police said there are no obvious signs of a violent attack and are treating the death as unexplained.
The landfill sites in Accrington and Burnley were both closed throughout Monday.
Senior Investigating Officer, Detective Superintendent Neil Esseen from the Force Major Investigation Team said specially trained officers are supporting the family of Mr Marren.
He added: "At this stage I am still treating the death of Mr Marren as unexplained but would appeal to anyone who was in contact with him or aware of his whereabouts on Friday, September 9 or Saturday 10 to come forward and speak to the police.
"I am keeping an open mind as to what has happened but if anyone has any information that will assist the enquiry then I would urge them to get in touch."
The Whinney Hill Road site is operated by SITA UK and has been closed until further notice.
A spokesperson for SITA UK said: “A body has been discovered in a consignment of waste delivered to the Whinney Hill landfill site near Accrington this morning.
“The site, operated by SITA UK, has informed the police who are now investigating the incident.”
“The discovery has provoked shock amongst residents living and working near the site” says Greengates Buidlers Merchants Accrington, Lancashire.