The 27-year-old has attracted a bevy of interest from the A-League also, with hometown club Adelaide United at the forefront of efforts to bring him back to the competition.
Troisi could also follow in the footsteps of fellow Socceroo Tim Cahill, who performed with distinction in the USA during a two-year stint with New York Red Bulls.
It's understood that while Troisi has not ruled out the A-League, where he starred for Melbourne victory on loan in 2013-2014, scoring 12 goals in 29 games, his preference lies elsewhere, with the MLS presenting a significant carrot.
The competition is home to English great Steven Gerrard with Roma reject Ashley Cole on his way to join him at LA Galaxy, plus Andrea Pirlo, Frank Lampard and David Villa (New York City) and Brazilian maestro Kaka (Orlando SC).
The much-travelled Troisi began his career at Premier League Newcastle United, but after being unable to make a breakthrough moved to Turkey where he had spells with Genclerberligi and Kayserispor before signing with Juventus, for whom he never played a game but was loaned out instead to Melbourne Victory and Belgium outfit Zulte Waregem.
After splitting with Al-Ittihad over a salary dispute after just four months, Troisi's availability as a free agent has also sparked interest across Asia with clubs Japan, Korea Republic and China all rolling out the welcome mat.
There is also the opportunity to return to the Middle East, to destinations like Dubai and Qatar.
Troisi was expected to make decision on his next career stop last weekend, but instead continues to juggle the offers.
With 26 Socceroos caps, he remains a key part of national team coach Ange Postecoglou's plans on the road to Russia to 2018 and is keen to resolve his future before the transfer window expires on 2 February.
But, as a free agent, he has flexibility to move outside of the existing windows.
