But the couple's lawyer says that Ritz, who is also member of Parliament for Battlefords-Lloydminster, appears not to be familiar with the legal procedure.
Haidah Amirzadeh says if the appeal is withdrawn it would basically kill the application.
Waheeda and Ashfaq Afridi have spent three years trying to get the little boy named Ajjab to Canada.
He is the son of Waheeda's sister, who is a widow struggling to raise her six other children.
Saskatchewan officials have said they support the child coming to the province and are encouraging Ottawa to allow it.
Amirzadeh said the Afridi family submitted the application to Ottawa before the federal government decided in 2013 to stop accepting adoptions from Pakistan.
Speaking to talk show "John Gormley Live" earlier this week, Ritz said the federal government has received the signed letter of no objection from the province but it is only “the start of the process.”
When asked by Gormley whether Immigration Minister Chris Alexander could expedite the process if the appeal was discontinued and a new application was submitted, Ritz answered “yes.”
“If your friend, the lawyer, wants to withdraw the appeal, things can change a little more dynamically than they have now,” Ritz said.
Kevin Menard, communications specialist with Citizenship and Immigration Canada, said it would be inappropriate to comment on a matter currently before the courts.
“We will reach out to the province to seek written clarification on what their official stance is on Pakistan adoptions,” Menard said. "If a new application were submitted, the letter of no objection would have to overcome all legal concerns raised by the provinces when they decided to cease adoptions from Pakistan in July 2013."
Waheeda Afridi, who has been a Canadian citizen for nearly a decade, has been living abroad to care for the boy since his birth in 2010.
Amirzadeh said Waheeda is in ill health and needs to return home to Saskatoon as soon as possible.