The team values him as a mentor for rookie Jaren Jackson Jr., and Conley was not eager to be dealt, a separate ESPN report added.
The Raptors are the latest Eastern Conference team to make a big trade.
The Memphis Grizzlies may ultimately decide they would have more options to deal Conley closer to the draft.
Miles, who turns 32 in March, is averaging 10 points per game off the bench for Toronto. He spent 11 seasons with the Grizzlies and is the franchise's all-time leader in points, rebounds, blocks and made field goals.
Wright (6-5, 183), who will wear jersey #2, has appeared in 49 games (two starts) and has averaged 6.9 points, 2.6 rebounds and 2.2 assists in 18.3 minutes while shooting 43.3 percent from the field, 33.3 percent from three-point range and 86.9 percent from the free throw line this season.
Gasol, 34, is averaging 15.7 points, 8.6 rebounds and a career-high 4.7 assists in 53 games this season. They added an elite centre in Marc Gasol, and according to Masai Ujiri they are not done adding pieces for the playoff run.
Once the captains got down to the real serious business and all was said and done, Raptors stars Kyle Lowry and Kawhi Leonard found themselves as opponents, as the former was selected as a reserve for Team Giannis, while LeBron used one of his starter selections to pick Kawhi.
Gasol has a $25.6 million player option for next season.