Conley has spent his entire 12-year career in Memphis.
Gasol heads north of the border averaging 15.7 points with 8.6 rebounds per game.
The Grizzlies have been looking to unload Gasol and Mike Conley Jr., as the team looks to rebuild.
Gasol, 34, represents an upgrade at the centre position for the Raptors.
Utah Jazz GM Dennis Lindsey and his brain trust have reportedly been aggressive in their attempts to upgrade the team's roster ahead of Wednesday's National Basketball Association trade deadline.More news: Trump tells Congress - and Sanders - 'America will never be socialist'
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Valanciunas was tied with Kyle Lowry as the Raptors' longest-tenured player, making his debut during the 2012-13 season after being selected fifth overall in the 2011 draft.
"That's our goal and I think everybody on the team understands that and we'll keep trying to achieve that goal".
Conley had been linked to Utah, Detroit and even Toronto along with Gasol in a handful of reports.
Gasol also has a highly-decorated global career as a member of the Spanish National Team, where he has played for Raptors assistant coach Sergio Scariolo.
Valanciunas hasn't played in almost two months after suffering a dislocated thumb, but is ready to return to the lineup.
Ennis, 28, was averaging 7.4 points and 2.8 rebounds in 39 games (25 starts) during his first season in Houston.
Valanciunas has been out since mid-December with a thumb injury but was going to make his return Thursday night against the Atlanta Hawks. But three of the four Raptors who played the most minutes against the Cavs last May - DeMar DeRozan, Miles, and Valanciunas - are now all gone.