Mr Annang-La told the Ghana News Agency at the Kpone site that the landfill site was overly stretched due to the amount of refuse deposited daily.
He was speaking after fire-fighters of the Ghana National Fire Service put out a ravaging fire at the Kpone site on Sunday.
The MCE, in the company of some other officials of the Assembly, explained that the TMA was collaborating with Zoomlion Company Limited to relocate the landfill site from Kpone to Sege.
Assistant Divisional Officer (ADOII) Bright Nana Sarfor of the Devtraco Fire Station said the office received a distress call at about 1430 hours about the fire at the Kpone landfill site.
He said preliminary investigations showed that the fire outbreak might be from the activities of scavengers.
He said the scavengers set the fire to help them unravel cables and other materials for sales but forgot to put out the fire, which spread to other parts of the site.
ADOII Sarfor said three fire tenders from Tema Industrial area and the Devtraco Fire Stations dealt with the outbreak.
He called on authorities to regulate the activities of the scavengers to prevent future outbreaks.