Behich has been heavily linked this week with a move from the A-League to Turkish club Bursaspor.
Turkish media reports again suggested on Friday the 22-year-old was on the radar of the Super Lig outfit, and could soon be playing with the club.
But Aloisi, who has already lost a string of players overseas - most recently Socceroos fullback Michael Marrone to China - would far prefer to keep the left-back until the end of the A-League season.
And he also believes that's best for the youngster's career, confident there would be multiple offers from good overseas clubs if Behich bides his time.
"I know there's been some offers," Aloisi admitted. "(If it's) up to me, Aziz isn't going until the end of the season.
"But I don't make the final decision. If the club gets a massive offer, that's a different story.
"I've had a chat with Aziz, and I still believe that if Aziz keeps on playing the way he's playing, and keeps on improving his game, there'll be a number of clubs lining up.
"At the moment, I don't want to lose another player. We've lost quite a few players this season already. Aziz is too important for us to lose now."
Short-term at least, Aloisi will have to find a replacement for Behich.
He is suspended for Heart's vital match against Western Sydney Wanderers at Parramatta Stadium on Saturday night having exceeded his yellow card limit.
Aloisi says he's considering several possible options, with ex-Perth Glory 20-year-old Sam Mitchinson the most likely having impressed at left-back previously when Behich has been on Socceroos duty.