Abd Allah made the proposal during talks in Amman on Wednesday with visiting Canadian Housing and Labour Minister Joseph Fontana, the agency said.
The king on Wednesday said that "measures should be stepped up to set up a free trade agreement with Canada aimed at bolstering the Jordanian economy".
Jordan, a member of the World Trade Organisation, was the first Arab country to sign a free-trade agreement with the United States, in 2000, and with Singapore, in 2004.
Amman also has an association agreement with the European Union.
Abd Allah and Fontana discussed possible Canadian assistance to develop the first mortgage company in Jordan aimed at providing low-income housing as well as investment schemes for Canadian businessmen in Jordan, the agency said.
Fontana, who arrived on Tuesday in Jordan for a two-day visit, also met the board of directors of the private firm United Arab Investors to kickstart the mortgage company, Petra and the Canadian embassy said.
The embassy said Fontana was accompanied by an expert from the Canadian Mortgage and Housing Corp to conduct a detailed feasibility study on the creation of a local mortgage insurance facility.
Fontana also had talks with Jordanian Housing Minister Amjad Majali and Prime Minister Faisal al-Fayiz.