The remains were found by a passer-by and are thought to be that of a white man, who had been dead for several days.
A GMP spokesperson said there had been “further breakthroughs” and police now had “four current scenes in place”.
They included Worsley Road in Winton, Blackleach Reservoir and Linneyshaw Colliery Wood in Salford, along with Mitchell Street in Bury.
In a statement, police said the cordons were to “preserve any evidence found while also making sure we leave no stone unturned”.
Det Supt Lewis Hughes added GMP had been “trawling through hundreds of hours of CCTV, alongside recording several accounts from the public”.
“The four scenes in place are to make sure we investigate thoroughly and continue with our good progress,” he said.
He continued to appeal for anyone with information to contact them.