Treliving said Aug. 2 that he expected Tkachuk would be signed by the time training camp opens Sept. 14.
"That's been our expectation, our hope, our goal," he said. "That's what we're working toward. I know that's what Matthew wants as well. We've got to keep working away at it and get to the point where we can get a deal done that works for everybody."
Tkachuk is one of several high-profile restricted free agents who remain without a contract, including forwards Patrik Laine and Kyle Connor (Winnipeg Jets), Mikko Rantanen (Colorado Avalanche), Brayden Point (Tampa Bay Lightning), and Brock Boeser (Vancouver Canucks), and defensemen Charlie McAvoy (Boston Bruins), Ivan Provorov (Philadelphia Flyers) and Zach Werenski (Columbus Blue Jackets).
Giordano, entering his 14th NHL season, all with Calgary, said he is looking forward to being teammates with forward Milan Lucic, who played the past four seasons for Pacific Division rivals (Los Angeles Kings, 2015-16; Edmonton Oilers, 2016-19).
"I think everyone knows that he's a presence out there," Giordano said. "I've played on a lot of different teams, and every time you have a guy with that sort of presence out there, it makes everyone else feel better about their game, better about themselves, and a little bit more comfortable. … Hey, listen, playing against [Lucic] for a lot of years, he's a game-breaking type of guy who plays well in the big games. He has a lot of experience, obviously, so he's going to be a leader for us and really help our team."
Lucic, acquired in a trade with the Oilers for forward James Neal on July 19, scored 16 goals in 161 games the past two seasons for Edmonton after scoring 23 in 82 games in his first season with the Oilers. He has 501 points (198 goals, 303 assists) in 890 games with the Oilers, Kings and Bruins.