The person spoke on the condition of anonymity because of the sensitive nature of the negotiations.
Turkoglu's agent, Lon Babby, didn't immediately return calls or e-mails.
The 6-foot-10 forward who helped the Orlando Magic to the NBA finals arrived in Portland on Thursday to meet Blazers executives and tour the city. He was scheduled to leave on Saturday.
A source close to the talks told Yahoo! Sports on Friday night Turkoglu plans to sign with the Toronto Raptors.
He opted out of his Orlando contract last week when the team acquired Vince Carter from New Jersey. Turkoglu was due $7.3 million next season in the final year of his $36 million, six-year deal with Orlando. He averaged 16.8 points and 5.3 rebounds last season.
Earlier Friday, there were reports that Turkoglu had agreed in principle with the Blazers.
Turkoglu, from Turkey, is a nine-year NBA veteran. He played for Sacramento and San Antonio before signing with Orlando as a free agent in 2004.
This season he often ran Orlando's offense and created matchup problems for the Celtics and Cavaliers in the playoffs. Against the eventual champion Los Angeles Lakers in the finals, Turkoglu averaged 18 points.
He was said to be seeking a long-term deal worth at least $10 million annually. Toronto had also expressed interest in him.
The Blazers are looking to bolster a team that won 54 games last season and advanced to the playoffs for the first time since 2003.
Anchored by All-Star guard Brandon Roy and LaMarcus Aldridge, the Blazers were the second-youngest team in the NBA.