The Portugal international could seek a move abroad in July after negotiations with the Sao Paulo-based outfit over extending the striker's stay broke down
The 34-year-old Portugal international, who joined the Timao from Sporting Lisbon last January, has just three more months remaining on his contract.
Corinthians are willing to offer an extension for only one year, but Liedson's agent has been holding out for a two-year contract, according to Globo Esporte.
If a deal is not reached, the striker, who has been linked with a return to old club Sporting, will be free to leave on July 31.
The Sao Paulo-based club are understood to be reluctant to offer Liedson a longer deal, citing his age and his poor goal return this year.
Liedson has scored 25 goals in 54 league apperances for Corinthians. He has been capped 14 times by Portugal, for whom he has netted four times.