After winning the Formula 3 and Formula 2 titles in consecutive years, Piastri has been serving as Alpine's reserve driver this season in tandem with an extensive private testing programme.
With two-time F1 world champion Fernando Alonso widely expected to continue his stint with Alpine beyond the end of the season, and Esteban Ocon under a long-term contract, the team has expressed an openness in loaning Piastri out to another team for next year.
Williams has emerged as the most likely destination for Piastri next year, likely replacing Nicholas Latifi, who has struggled to match new team-mate Alex Albon's form so far this season.
Speaking in Saturday's press conference ahead of the Canadian Grand Prix, Szafnauer said that Alpine had "some options" on Piastri that meant there was "no need to hurry" deciding on his future.
"We'll take our time and at the right moment within the silly season we'll have a look around and make those types of decisions," Szafnauer added.
Asked if he thought Piastri would be racing in F1 next year, Szafnauer replied: "Yes."
But Szafnauer was coy about any agreements already being in place, saying: "We don't talk about the details of our contracts we have with the drivers, that is something we never do.
"So as much as I'd like to tell you, I don't think I can, but what I do say is yes, that's the plan [for Piastri to race in F1 next year]."
Williams F1 boss Jost Capito acknowledged that Piastri was "ready to go into Formula 1" and was "one on the list for sure", but thought it would be "not just for us" through the wider silly season.
Latifi's struggles through the early part of this season have led to suggestions he could be replace by Piastri midway through the current campaign.
But Capito said that Williams would see out the year with its existing line-up given the contracts that are in place.
"We don't have any other plans," Capito said. "Both have a contract for the season, and our plan is to fulfil that."
Asked by Autosport about the speculation linking Piastri with a mid-season debut for Williams, Szafnauer said: "I've read the same and it is hard for me to predict the future on that, and I'd like not to.
"But I don't have any more knowledge than you do."
