Carter, a 26-year-old, 6ft 4in playmaker, was sacked by his Austrian club Oberwart on Wednesday after the escalation of a dispute which began when they deducted wages for time he spent with the national team.
He said yesterday: "I'm leaning more towards a move to Italy, but need to know more about their team and how I would fit in.
"Trieste are pushing for promotion to A1, which the Italians plan to expand next season anyway."
He confirmed his agent had spoken with both Giants and Towers and did not completely rule out a move to the Budweiser League. "Other factors come into the equation with a move to England. I know more about the clubs and the players and it would obviously be a lot easier to settle.
"But I have only four months of this season left and have to make the right move. There's a great deal more exposure in Italy and even in A2 the standard of basketball is probably better."
Carter has never played for an English club after moving straight to the Continent after completing his American college education.
Two new American signings who will not play this weekend are Justin Phoenix and Adam McCanna. Neither Phoenix (Birmingham Bullets) nor McCanna (Worthing Bears) will receive work permits in time.Reuse content