Stamkos has yet to play in the 2020 Stanley Cup playoffs as he rehabs from an undisclosed lower body injury. The Lightning face the New York Islanders in the Eastern Conference finals, with Game 1 on Monday.
Last week, general manager Julien BriseBois left open the possibility of Stamkos returning at some point during the playoffs and Cooper said on Sunday that he would update the media if anything changes during the Islander series.
"Everybody wants him to play and he wants to play, but as of now ... you get caught up in the collective momentum of how we're doing things and everybody's just pushing each other," Cooper said last week. "He's just as big a supporter of our group as anybody and so it's good to see."
Stamkos, 30, has not appeared in a game since Feb. 25, and he underwent core muscle surgery on March 2. He was given a six- to eight-week recovery timeline.
The center joined his teammates for Phase 2 voluntary workouts in June. He didn't participate fully during training camp, though he did join the team for some drills, including on the power play.
"Anytime you have a surgery there's going to be things that are certainly connected with one another," Stamkos told reporters on July 27. "There was a stretch for four to five weeks when I was skating when I was feeling really good. Obviously, there was no contact and no game-like situations during that time, so I was feeling good. Then I hit a little rut. Definitely all related."
Stamkos was second on the Lightning this season with 66 points (29 goals, 37 assists) in 57 games, trailing only Nikita Kucherov.
Kucherov, the 2019 Hart Trophy winner, was injured during Game 5 of the Lightning's second-round series-clinching win against the Boston Bruins. Cooper said Kucherov would be available for Game 1 against the Islanders.