The 27-year-old has been linked with a number of A-League clubs during the January transfer window, and he told the Herald Sun on Tuesday that both Phoenix and home-town club Adelaide have called him about signing.
Troisi last played in the A-League in the 2013-14 season, scoring 12 goals in 29 matches for Melbourne Victory, and it is understood his former club is also keen.
"They [Al Ittihad] were in breach of contract and I chose to terminate," Troisi said.
"A few clubs interested but nothing concrete but want to make decision in the next or so, ideally as soon as possible. But I won't rush into a decision for the sake of it.
"Victory was great to me, I enjoyed my time there and I stayed in touch with people there.
"I've had contact from [Phoenix coach] Ernie Merrick and [Adelaide chairman] Greg Griffin, and there's still interest overseas. I'll weigh my options up in the next week or so."
If Troisi was to sign for Victory, it seems unlikely the reigning champions would be able to have him under the salary without releasing another player.
Otherwise Victory could sign him as a guest player if Football Federation Australia deemed his international experience and profile to be sufficient.
Troisi has played 26 matches for Australia, scoring four goals, including the extra-time winner in last year's Asian Cup final.
Guest players can play up to 14 A-League matches and their salaries are exempt from the salary cap.
Phoenix need another attacking option with Roy Krishna out for three months with a foot injury, while the Reds' attack would benefit immensely from Troisi's versatility.
Troisi can play up front, as a number 10 or out wide.
Speaking to the Adelaide Advertiser, Reds chairman Greg Griffin confirmed the club are keen on the Socceroos attacker.
"James is an outstanding young man," Griffin said.
"It was really very interesting to go and talk to him about where we thought we could go with him and his own views.
"We all know James has no shortage of suitors.
"We've suggested we're a really good option for him, we'd love to showcase him."
Troisi has played for five different clubs in the last five seasons.