Baird said Canada has been working hard behind the scenes to win the release of the Al Jazeera journalist who will be entering his 13th month in captivity by the time Baird arrives in Cairo in January.
Baird has met twice with his Egyptian counterpart in the last month, most recently in Bahrain, and pushed for the release of the 40-year-old Fahmy, the minister's office said Tuesday.
"We had a long conversation about this," Baird told Ottawa radio station CFRA in an interview Tuesday about his most recent discussion with Egyptian Foreign Minister Sameh Shoukry.
Baird said he also met with Egypt's ambassador to Canada on Monday to discuss Fahmy's possible release.
Baird's office said the minister also had a separate conversation with Shoukry at an international gathering in the United Arab Emirates last month.
As Baird told the Ottawa radio station, there has been an ongoing diplomatic effort to free Fahmy, who was arrested on Dec. 29 last year along with two colleagues, Australian correspondent Peter Greste and Egyptian producer Baher Mohamed.
"We're doing a lot, everything we can. We're going to it in an effective way, not in a loud way," Baird said.
"We'll continue to make our case directly to the senior leadership in Cairo."
After a trial that was denounced as a sham, Fahmy was sentenced to seven years in prison for supporting the banned Islamist Muslim Brotherhood group of ousted Egyptian president Mohammed Morsi. Greste were sentenced to seven years in prison, while Mohamed was sentenced to 10 years.
They were also charged with fabricating footage to undermine Egypt's national security.
The journalists deny the charges, saying they were just doing their jobs.
Fahmy's family and others have suggested the case has political overtones, claiming Egyptian authorities believe Al Jazeera is biased towards the now-deposed Morsi and his Muslim Brotherhood.
The Qatar-based broadcaster denies the allegation.
Fahmy's family is hoping for a positive result after his appeal is heard on Jan. 1. His relatives have started an online crowdfunding campaign to raise funds for his legal fees.
Fahmy's family hopes he will be at least temporarily released on health grounds because he has hepatitis C and an injured shoulder.
Baird expressed muted confidence in securing Fahmy's release because of success in October 2013 winning the release of two other Canadians arrested in Egypt.
John Greyson and Tarek Loubani spent two months behind bars after their arrest and beating during an anti-government protest.
Both men had praised Baird, Prime Minister Stephen Harper, the country's diplomats and their friends, family and supporters for relentlessly pushing for their freedom.
"We had two Canadians that were imprisoned last year. We got them out through effective diplomacy," said Baird.