The games are the first for Canada since it crashed out of World Cup qualifying in an 8-1 defeat in Honduras in October. Stephen Hart, despite support from his players, resigned days later as coach.
The search for his replacement is ongoing.
The Canadian men, currently ranked 60th in the world, are slated to play No. 22 Denmark in Tucson on Jan. 26 before facing the 27th-ranked Americans three days later in Houston.
With European-based players still in season, the Canadian squad will likely draw on MLS players and younger talent.
"We will not have a coach in place for the Jan. 26 game so we're looking to deal with that internally," Canadian association president Victor Montagliani said prior to Monday's announcement of the U.S. friendly.
"Our first priority is to get the right person and secondly we have a soft date of getting one before the Gold Cup (the CONCACAF championship, scheduled for July in the U.S.)
"By the same token if it's not the right person and we need to wait a little bit longer, that's fine."
That would also cover a scenario where the right candidate isn't available until later in the year.
"There's so many variables when you're looking at this," said Montagliani. "It's not your standard employment situation.
"If it's the right person and we know it, great. Obviously we'd like to get one in as soon as we can. But I think the key component has got to be the person that we think will push the program forward to the next level so we're ready for 2016 when we do battle again."
That's when the next round of World Cup qualifying starts.
At its recent board meeting, the Canadian Soccer Association established some timelines for filling the job, starting with creating a short list in the new year.
"We've had a significant amount of interest from all over the world," Montagliani said.
With six top CONCACAF teams involved in the hexagonal round of World Cup qualifying in the region, which covers North and Central America and the Caribbean, the 2013 Gold Cup will take somewhat of a backseat.
But the 2015 edition of the CONCACAF championship has extra significance because the winner will advance to the Confederations Cup. It may also mean a trip to an expanded Copa America in 2016.
The Canadian men's team will hold a camp south of the border Jan. 19-30 around the Denmark and U.S. exhibition games.
Montagliani said newly appointed technical director Tony Fonseca, whose resume includes both Olympic coach and senior assistant coach, will not serve as interim coach.
"He's got a massive job on his hands ... He's already started that in earnest," Montagliani said of Fonseca's role as technical director.
He declined to name possible caretaker coaches but said they would either come from internally or "someone that has experience with the Canadian Soccer Association."
Nick Dasovic is currently tied up with the under-20 team, which is preparing for a CONCACAF qualifying tournament Feb. 17 to March 1 in Mexico.
The Olympic team coaching job is vacant since Fonseca switched roles.
The Houston game is the only outing for the U.S. before it kicks off its final round World Cup qualifying Feb. 6 in Honduras.
"The match against Canada will come at the end of an important training camp as we get players ready for the World Cup qualifier against Honduras, and also get a good look at some up-and-coming players in the national team pool," said U.S. head coach Jurgen Klinsmann said in a statement.
"Obviously we have a great history with Canada, and they were unlucky not to qualify for the final round."
U.S. Soccer celebrates its 100-year anniversary in 2013, just as Canada did this year. The two teams played to a 0-0 draw at Toronto's BMO Field in June as part of the Canadian 100th year celebrations.
That extended the Americans' unbeaten string against Canada to 15 since a 2-0 loss in Vancouver in April 1985.