The Foxes were rocked last year when young players Tom Hopper, Adam Smith and James Pearson were sacked following an ugly incident during the club's tour of Thailand.
All three were dismissed after a club investigation into allegations that they racially abused women with whom they were engaging in sex acts in a hotel room, while on a post-season trip to the country.
Aiyawatt, the son of Leicester owner Vichai, wants the team to return to Thailand following their remarkable Premier League title winning campaign.
"I want them to see the Thai people, how welcome they are," Aiyawatt said.
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"They are massive now and they want to say thank you to the Thai fans.
"The players need privacy as well, but I've talked to them and they know they need to treat everything well.
"You are popular, that is great, and people come to see you because they admire you and they want to talk to you. They will talk to you like you're their son, so be proud and enjoy it. Don't just think about the privacy time."
Pearson's dismissal paved the way for the appointment of Claudio Ranieri, who transformed Leicester from 5,000-1 outsiders into kings of English football.