Although a verbal commitment may be announced sooner, the terms of the contract cannot be finalized until Wednesday, when the NBA informs teams what the 2009-10 salary cap will be.
Turkoglu, a 6-10 forward from Turkey who played a prominent role in the Magic's recent trip to the NBA Finals, had been looking for a five-year deal in the neighborhood of $50 million.
Experts believe the cap likely will be somewhere between $57 million and $59 million. If the cap number comes in at the high end, the Blazers can offer close to what Turkoglu is hoping for.
After having dinner with Trail Blazers coach Nate McMillan in Florida on Wednesday, Turkoglu flew to Portland on Thursday to visit the team and see the city.
ESPN's Ric Bucher reported that the Turkish star remained in Portland on Friday, where he and the team were working on a deal.
The Blazers, one of the youngest teams in the NBA, had been intent on adding experienced players this offseason. They targeted the 30-year-old Turkoglu as a player who could take pressure off team leader Brandon Roy, who has carried the burden of creating most of the team's scoring opportunities.
Henry Abbott writes the TrueHoop blog for ESPN.com.