Tkachuk, a restricted free agent forward, led Ottawa with 36 points (17 goals, 19 assists) in 56 games last season. He was second in the NHL with 220 shots on goal (Auston Matthews, 222) and with 248 hits (Radko Gudas, 250).
"We have had really positive talks," Dorion told 590 The Fan on Thursday. "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."
Selected by the Senators with the No. 4 pick of the 2018 NHL Draft, the 21-year-old has scored 125 points (60 goals, 65 assists) in 198 games.
The Senators agreed with restricted free agent forward Drake Batherson on a six-year, $29.85 million contract ($4.975 million average annual value) on Sept. 3.
Ottawa also signed coach D.J. Smith to a two-year contract July 28, 16 days after Pierre McGuire was hired as senior vice president of player development to work with Dorion and owner Eugene Melnyk.
The Senators (23-28-5) finished sixth in the seven-team Scotia North Division and missed the Stanley Cup Playoffs for the fourth straight season last season.
Dorion said the rebuilding effort to become a consistent contender for a playoff spot needs to move to the next phase now.
"We just can't be satisfied with bringing a good effort every night," he said. "Now we've got to start winning games. And that's the way I look at it. We're still a young team, we're still progressing. But my statement about saying the rebuild is over is no more excuses about the rebuild. And that goes to our coaching staff and myself. Let's take the next step as a team, whatever that may be, wherever that takes us. Games that we should have won last year, whatever the reason, we have to win them this year."
