Holland, the GM of the Detroit Red Wings for 22 seasons before coming to Edmonton, said he's keeping all options open with Puljujarvi.
"I've had players tell me that in Detroit and they did play for Detroit," Holland said. "We've talked to a lot of teams. I'm not sure where I'm at. I'm not sure where it's going to go."
Though trading or re-signing Puljujarvi is an option, for the Oilers to add a legitimate scoring threat they will likely have to trade players to create salary cap space. But their options at forward are limited with forward Milan Lucic, who scored six goals in 79 games, signed through 2022-23.
They do have attractive candidates at defenseman with Oscar Klefbom, who is signed through 2022-23; Matt Benning, who can become a restricted free agent after this season; and Adam Larsson, who can become an unrestricted free agent after 2020-21, but Holland said any decision will be based on what's good for Edmonton, not just next season, but in the long run.
"Until there's something that I think makes really good sense to our team, I won't pull the trigger," he said. "On the short term, we want to compete for the playoffs in '19-20, but on the longer term ... I'm trying to oversee and build this team to be a really good, elite team in the Western Conference. We made decisions today based on those plans."
It doesn't appear the Oilers want to consider trading some of their defenseman prospects, but they may have to include them in potential deals to get the scorer they need. In the system they have Philip Broberg, the No. 8 pick of the 2019 NHL Draft; Evan Bouchard, the No. 10 pick of the 2018 NHL Draft; Dmitri Samorukov, the No. 84 pick of the 2017 NHL Draft; and Caleb Jones, Ethan Bear and William Lagesson, who each played for Bakersfield in the American Hockey League last season. Holland referred to the group as potential top-four defensemen.
"There are some young players that are going to need some time, but I think they can be real important players to this team going forward," Holland said.
And though the Oilers were quiet Monday, Holland said they will eventually have the chance to add free agents.
"Somewhere down the road we're going to have a ton of cap space and we're going to make noise," he said.