Neill, who turns 35 next month, has been without a club since being released by United Arab Emirates side Al Wasl last month.
"I had a chat to him a couple of days ago to see where he's at football-wise and what he wanted out of the rest of the season, and he wants to play football," Aloisi said.
"He's watched quite a few games in the A-League and he could see what we're trying to do as a team. He likes the way we're trying to play football.
"He's still the national team captain and he wants to win games.
"It's great for us because we want to make finals and if you make finals you've got every chance of doing well in it."
Aloisi was an integral member of the Socceroos alongside Neill before he moved into coaching with the Heart.
"As former team-mates, he knows what I'm going to be like as a person, but he doesn't know what I'm like as a coach, so that's a little bit different," he said.
"When I did speak to him, I said what I expect from my players and what I'm expecting as a team and the way we want to play and he liked that.
"Now we have to see if he ends up putting pen to paper."
Aloisi said he had no doubts about the former Blackburn Rovers and West Ham United defender's physical state.
"He'd been playing until recently; he played 60 minutes for the national team against Romania, so his fitness is not a problem," he said.
"Lucas looks after himself physically and he's never really had any major issues injury-wise, so he's a fit guy."
Heart, fifth in the A-League table, tackle the seventh-placed Newcastle Jets in a crucial clash on Friday.
"Any result in Newcastle would be a positive outcome for us," Aloisi said.
"We haven't been great away from home, so it's time that we start picking up points because if we want to make finals you have to win away from home."
Aloisi said new signing Marcel Meeuwis had received his international clearance and was expected to feature.