"Messi at Inter? Why not?" Thohir told his club's official website.
Inter is currently enjoying a revival under the Indonesian, who bought a majority share from long-time owner Massimo Moratti in 2013.
This summer, Thohir sanctioned more than €70 million in transfer fees, the club's biggest spending spree in years. It has so far paid off. Despite scoring just 23 goals in 17 matches, Inter sits in first place heading into the Christmas break.
But Thohir is thinking about pulling off the coup of coups.
"Our strategy is clear - to return Inter to its rightful place as one of the top 10 clubs in the world," said Thohir. "We're building a strong, young team under Roberto Mancini - a team that is ready to challenge the best in Europe."
Messi's contract with Barcelona runs until 2018. He will be 32 years old by then - still a capable age in the game - and should he decide not to re-sign with the only club he has known as a professional, Inter could offer him a different experience.
It's not the first time Inter has thought about Messi. Former Barcelona president Joan Laporta confirmed in October that the Nerazzurri had attempted to trigger Messi's outrageous €250-million buyout clause.
"But I always said that the sale of the Argentine was impossible," Laporta said.
Former Argentina teammate Juan Sebastian Veron suggested that the interest may have been mutual.
"He once told me that he would like to play for Inter," Veron told Tuttosport. "But let me be clear: It is something that happened in the past. Moratti was still the owner. Frankly, to me, it seems impossible for Messi to leave Barcelona."