Worawi Makudi, president of the Football Association of Thailand, said he had been approached by Liverpool's representative, former England international Steve McMahon, with a view to setting up the club's third visit to the kingdom in eight years.
"We've had a few meetings already and the visit is very likely to happen," Worawi told Reuters.
"We have so many Liverpool fans in Thailand, this will be great for them and great for Thai football."
If confirmed, the Reds will take on the Thai national team, whom they played in 2001 and 2003 in Bangkok.
Liverpool are also eyeing their first match with the Singapore national team, although negotiations are not yet complete.
"Nothing has been finalised yet," an official from the Football Association of Singapore told Reuters.
"But we have been approached several times by representatives of the Premier League club and we are now in talks."
Lam Shing Kui, general secretary of Hong Kong's soccer federation confirmed Liverpool's interest and told the South China Morning Post: "We are still working out the details. If Liverpool come they will play against the Hong Kong team."
If the mooted tour goes ahead, Liverpool will follow rivals Manchester United, who are scheduled to visit China, South Korea, Indonesia and Malaysia in July.
Liverpool are third in the Premier League behind United and Chelsea having topped the table for much of the season.
