The Melbourne-born Greek international is set to arrive in Brisbane this weekend after stints with J-League side Jubilo Iwata and China's Shanghai Shenhua, having signed as an injury replacement player for Daniel Bowles.
The 32-year-old centre-back was identified by prosecutors in 2011 for alleged involvement in the so-called 'Koriopolis' match-fixing scandal during his time at Olympiacos but has never been charged.
Sydney FC reportedly turned down the chance to sign Papadopoulos in January because of the links, but Aloisi was comfortable with the move and said he had not and would not discuss the matter with the player.
"It's not a concern - it's five years ago and, again, allegations," Aloisi told reporters on Friday.
"FIFA haven't suspended him, no competition's suspended him, so obviously it's not that serious. It's serious for you guys (the media). For me, it's not.
"Lucky enough I know quite a few people over in Greece and I was able to ask what he's like as a person - good person.
"That's what we want at the football club - an experienced player that's played in Asia, which is important for us, because we're in the Champions League.
"He also captained a massive club in Olympiacos. He's not only a good player, he's a good leader. We're happy."
Capped 36 times by the Greek national team, Papadopoulos looks on paper to be a shrewd signing.
He has an Australian passport, meaning he won't be counted as an import and is eligible to play for the Roar in both the A-League and the AFC Champions League.
Aloisi could offer him a longer-term deal if he impresses during his time at the club.
"It's hard to say exactly what condition he's in but we'll see that when he arrives and take it from there," he said.
"We've still got 14 games left without finals and without getting through to the next stage of the Asian Champions League, so there's still a lot of football to play."