The Verdao chief had initially ruled his side out of the race for the creative attacker, but then confessed that he would be open to signing the ex-Barcelona star
The 32-year-old is currently on the lookout for a new club after unilaterally rescinding his contract with Flamengo on Thursday as a result of unpaid wages.
Questioned about the possibility of signing Ronaldinho, Tirone had initially stated that Palmeiras had no desire in acquiring the player, only to retract his comments just hours later.
"Every big player is interesting, and Ronaldinho is a star," Tirone told Radio Transamerica. "But our financial reality is difficult, we will have to wait and see what happens."
Palmeiras were one of the three clubs, along with Flamengo and Gremio, who tried to sign Ronaldinho in early 2011 when the former Barcelona star left AC Milan.