The district police, which is probing the matter, is of the view that since it is a "big issue" a specialised agency like the EOW should inquire into it.
"The tender system of the Rashtriya Nirman Nigam was faulty as payments from Rs 4.24 lakh to 71 lakh have been made for elephants and it is a very big issue," DIG (Lucknow) Ashutosh Pandey said.
There were about eight firms which had supplied stone structures for Noida and Lucknow, he said adding recommendation for an EOW inquiry would be sent soon.
Director General of Police AC Sharma, when contacted, said, a request for EOW inquiry has to be made by the district police and so far it has not been received.
"If we receive a request in this regard, further action on handing over the probe will be taken," the DGP said. Earlier in the day, Akhilesh had said the alleged financial fraud could be to the tune of Rs 40,000 crore.
The district police had yesterday carried out searches at the office of Rajkiya Nirman Nigam at Gomti Nagar in connection with alleged irregularities in installation of statues of elephants at parks in Lucknow and Noida.