Roberto Mancini's side lead Serie A after 17 games, having been transformed into potential title contenders following significant investment from the Indonesian as he aims to take the club back up into Europe's elite category.
And Thohir says the spending will continue, adding the Nerazzurri would not pass up the chance to make a stellar signing such as Messi should the opportunity arise to tempt him away from Camp Nou.
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"Messi to Inter? Why not! When he finishes his contract with Barcelona, he'd be a great signing," he said via the club's official Twitter account.
"Our strategy is clear: we want to take Inter to the place we deserve, among the best 10 clubs in the world.
"We're first in the standings after 17 games. We're a solid team, with a great desire to win.
"We're building a young, strong team, with the guidance of Roberto Mancini, to compete with the best clubs in the world."