Thorrington told ESPN that while the deal isn't done, LAFC has allowed Rossi to travel to Istanbul in anticipation that the deal -- which will consist of an initial loan period followed by an expected permanent transfer -- will be completed.
"We are close to finalizing [the deal]," Thorrington told ESPN. "There are a couple of T's that need crossing, I's to be dotted, etc.," he said. "But it looks like it is heading in that direction."
A source with knowledge of the deal told ESPN that if the transfer is completed, LAFC stands to gain somewhere around $10 million. LAFC will retain a percentage of any future sale, but will also have to pay Rossi's previous club, Uruguayan side Peñarol, a cut of the fee as well.
Fenerbahce later tweeted a photo of Rossi on a flight and stated that he will undergo a medical and "continue negotiations".
Thorrington stressed that developing young players and then transferring them for a profit has long been part of LAFC's process.
"I do believe that this is the next step that will lead to a long term move that opens up a lot of financial flexibility for us to add talented players," Thorrington added. "This has always been a part of our process. We remain committed to winning and everything that our operation does is with the idea of making us stronger and winning championships."
Rossi, 23 has long been rumored to move on from LAFC, but the coronavirus pandemic has put a damper on the world transfer market. Fenerbahce has been searching for a striker, but needs to move quickly. While the transfer deadline in Turkey is Sept. 9, the deadline for naming its roster for the Europa League is this Thursday.
Operating primarily on the wing, Rossi has been an impressive performer for LAFC ever since he arrived ahead of the 2018 season, scoring 57 goals in 120 league, playoff and cup appearances. During the pandemic-shortened 2020 campaign Rossi won the Golden Boot with 14 goals, was named to the MLS Best XI, and won the league's Young Player of the Year award.
Rossi has represented Uruguay at numerous youth levels, but has yet to make an appearance with the senior side.
If the deal is completed, Rossi would find himself in the same club as Mesut Ozil, Enner Valencia and Luiz Gustavo. They have won all three of their matches to start the 2021-22 league campaign thus far, and trail Trabzonspor only on goal differential.