The vase is one of four designed by William Burges in 1874 for the corners of the Summer Smoking Room, at the top of Cardiff Castle's clock tower.
Culture Minister Ed Vaizey has put a temporary export bar on the vase.
He said he hoped this would allow time for a buyer to come forward and "ensure this incredible piece by Burges remains in the UK".
He said: "The other three vases that formed this magnificent set are still in the UK and it would be fantastic to see them all reunited in an exhibition at Cardiff Castle or another of our public museums."
Mr Vaizey was recommended to defer granting an export licence until 27 August by the Reviewing Committee on the Export of Works of Art and Objects of Cultural Interest (RCEWA).
This date could be extended to 27 November if a serious intention to raise funds to purchase the vase is made.
Sir Hayden Phillips, RCEWA chairman, said: "This Burges vase is intrinsically beautiful and outstanding in its historical significance."
A "historical" vase could be exported unless a UK buyer is found to match the £163,000 offered by a foreign buyer.