Holland said he was optimistic he and new coach Dave Tippett, who was hired May 28, could've helped Puljujarvi change his mind about leaving Edmonton.
"I was certainly hoping that coming here and being in charge, and with a new coach, and that we'd made some changes and Jesse would have maybe had a bit of a different thought about things given where he was at when the season was over," Holland said. "But nothing has really changed.
"I called [his agent] Markus Lehto [in late July] and talked to him at length, and he told us to feel free to call Jesse but that he had had multiple conversations with Jesse and said Jesse really feels strongly about his position. They, Jesse and Markus, the agent, they feel very strongly about wanting to move on."
Holland said he would not guarantee trading Puljujarvi by Dec. 1, adding he thinks it's a good thing he will be playing overseas.
"And I'm not worried about a time frame. We have until Nov. 30 for him to play hockey (in the NHL) this year. I think it's always tough for any player to miss all of NHL training camp, to be sitting around and just skating on your own, and then try to get up and running," Holland said. "For Jesse, when and if he comes back to the NHL in the '19-20 season, it's going to be easier to get up and running quicker if he's playing on a team and practicing every day and playing on a regular basis."
Edmonton (35-38-9), which finished 11 points behind the Colorado Avalanche for the second wild card into the Stanley Cup Playoffs from the Western Conference last season, has missed the playoffs in 12 of the past 13 seasons.
NHL.com staff writer Tim Campbell contributed to this report