The 22-year-old forward is the lone unsigned restricted free agent in the NHL. He led the Senators with 36 points (17 goals, 19 assists) in 56 games last season.
Ottawa opens the regular season against the Toronto Maple Leafs at home Oct. 14.
"We were hoping, obviously, that he'd be here by now," Senators coach D.J. Smith said Tuesday. "As coaches, you know these things can linger on and you kind of put lines together in the back of your mind thinking, 'When Brady gets here, thinking this is going to happen, this is going to happen.'
"Well, we're at the point now, we only have two [preseason] games left, so I got to start preparing like he's not going to be here. So that changes things. And obviously he's a huge piece to our team, but that's not my job. My job is to coach the guys that are here, and when he gets here, I'll coach him. So we're going to put the best group out there and we're going to do everything we can as a group."
Ottawa general manager Pierre Dorion told 590 The Fan on Sept. 10 that he expected Tkachuk to be signed before the start of training camp Sept. 22.
"We have had really positive talks," Dorion said. "Are we confident he'll be signed by the time camp starts? Yes. These negotiations aren't always easy. They take a bit more time."
Tkachuk, the No. 4 pick in the 2018 NHL Draft, was second in the NHL last season with 220 shots on goal (Auston Matthews, 222) and 248 hits (Radko Gudas, 250). He has scored 125 points (60 goals, 65 assists) in 198 NHL games.
Center Colin White will be out for "a significant amount of time" with a shoulder injury, Smith said. He left a 3-1 loss to the Maple Leafs on Monday at 4:58 of the first period and was scheduled to have an MRI.
"It doesn't look good at this point," Smith said. "We're waiting on results.
"That hurts us. He's a guy that's been in the League that can play on the power play, can take right draws. When he's going, he can get to the net. He can do a lot of things, and now you find yourself in a spot where you're a little thin there, especially if another injury were to happen. We'll have to figure that out and we will."
