Bristol City Council has said on Friday that removing the Black Lives Matter activist sculpture from the plinth where the statue of slave trader Edward Colston once stood could cost thousands of pounds.
"We are waiting on a final quote from the contractors and police, but it is likely to run into the thousands", a council spokesman said.
"We should get the bill next week".
The black resin effigy of Ms Reid, called A Surge of Power, was created by London-based artist Marc Quinn, who said it was intended to be a temporary installation and a contribution to the anti-racism movement.
Quinn said he was inspired to create the statue after seeing an image of Ms Reid standing on the plinth with her fist raised during the Black Lives Matter demonstration 7 June, just after the statue of Edward Colston was torn down by protestors and thrown into the river.
Contractors took down the statue of BLM protestor Jen Reid on Thursday, a day after it was illegally erected in the middle of Bristol.