The new Nerazzurri chief insists the club can bring in anybody - as long as the finances are in order - but played down January arrivals with such a small window to make signings
The Indonesian, who acquired a majority stake in the Nerazzurri in 2013, had already joked about bringing the four-time Ballon d'Or-winning Barcelona forward to San Siro since taking over Massimo Moratti's role as chief.
Although Thohir says Inter are unlikely to make any major January moves due to the length and timing of the transfer window, he has pandered to supporters by suggesting that top footballers are within the Serie A side's reach.
"Players like Messi can be bought," he told Republika Online. "But only on the condition that the club's finances are not affected.
"In January, though, it will be difficult to recruit new players because the window is so narrow and there's only half a season left to play."
Walter Mazzarri's Inter side travel to Genoa on Sunday, with kick-off at 15:00CET.