Fischer added that Lowry is "aware" of the trade talks the Raptors are holding.
Per Fischer, the Grizzlies rejected Toronto's initial offer since they would prefer to receive draft picks and younger assets such as small forward OG Anunoby in a deal involving Conley and Gasol.
Michael Grange of Sportsnet reported that the Grizzlies initiated the offer to gauge the market on Conley and Gasol, but he noted that talks "did not progress very far."
At 38-16, Toronto is second in the Eastern Conference, and it trails the first-place Milwaukee Bucks by two games. While the Raptors are on track to reach the playoffs for the sixth consecutive season, postseason success has eluded them with just one trip to the Eastern Conference Finals and no NBA Finals appearances during their current run.
The 32-year-old Lowry has been a driving force behind the Raptors' recent playoff berths, as he has been named an All-Star in each of the past five seasons.
Lowry has struggled through injuries this season, however, and his shooting has suffered as well. In 42 appearances, he is averaging 14.1 points, 9.2 assists and 4.5 rebounds, while shooting 40.9 percent from the field and 31.9 percent from three-point range.
While Lowry is an All-Star this season and Conley still has yet to make an All-Star Game during his 12-year NBA career, Conley has arguably been the superior player this campaign. The 31-year-old veteran is having a career year with 20.3 points, 6.3 assists and 3.4 assists per game while shooting 43.5 percent from the field and 35.9 percent from beyond the arc.
Gasol, 34, is also having a strong season with 15.7 points, 8.6 rebounds and 4.7 assists per game. Of all the players in the reported trade proposal, Gasol is arguably the most accomplished with three All-Star nods and an NBA Defensive Player of the Year award to his credit.
Valanciunas is the youngest player in the mix at 26, but he remains out with a thumb injury that has limited him to 30 games this season. In those games, Valanciunas has averaged 12.8 points and 7.2 rebounds with a field goal percentage of 57.5 percent.
Contractually, Conley has one year remaining on his deal and an early termination clause for 2020-21, while Gasol can become a free agent at the end of the season if he opts out. Meanwhile, Lowry has one year remaining and Valanciunas can also hit free agency at the conclusion of the 2018-19 campaign.
If the Raptors manage to make the deal, it will have the feel of a win-now move since the combination of Conley and Gasol has been more productive than Lowry and Valanciunas this season. Adding Conley and Gasol to a core that includes Kawhi Leonard and Pascal Siakam would give the Raptors one of the NBA's strongest starting lineups.
As Fischer mentioned, the trade will likely depend on whether Toronto adds more to the deal.
Fischer also reported the Grizzlies are in discussions with other teams regarding Conley and Gasol, including the Utah Jazz for Dante Exum and Grayson Allen and the Detroit Pistons for Reggie Jackson.
This season may represent Toronto's best chance to win a title since Leonard can potentially leave via free agency during the offseason, so there is plenty of motivation to make a big move and establish itself as the clear top team in the East.