Enterprise Management Services has been named as the frontrunner to become Peterborough City Council's strategic partner.
The organisation would be involved in recycling, street cleaning and grounds' maintenance.
The council said a final decision would be made later this month.
Deputy council leader Matthew Lee said: "We are looking for a strategic partner to deliver some of our key frontline services for many years, so it's important that we get it right.
"I'm pleased to have two strong contenders in the final stage of this process and will consider the recommendation carefully before making my decision."
A council in Cambridgeshire has named its recommended preferred organisation to become its partner in the running of waste collection and other services.