He said Obasanjo deserves to be jailed if he has committed any crimes.
Last week, Obasanjo alleged that Buhari's administration has an active plan to indefinitely detain him by using false witnesses and documents to frame him.
Speaking on the public war of words between the former president and Buhari's administration, Oshiomole said he would arrest Obasanjo if he committed any offence just like he indiscriminately arrested people like him when he was president between 1999 and 2007.
He said, "He should be arrested if he has committed any offence. He arrested many of us. So, if we are celebrating Chief Gani Fawehinmi, we have compelling reasons to do so. In all of these, we didn't pay any money to Gani or Falana. They defended us pro bono.
"Gani is not here today, but his spirit is here. Falana is here and today, I am standing. Even the president who was in charge then, he is now complaining that they want to harass him. He was harassing me and he got me arrested.
"He thought he himself would not be arrested? If I were the president, I would arrest him. We are all Nigerians. I remember one day I told him, I said, 'President Obasanjo, we made you president. You did not make me a Nigerian. You are our creation; I am not your creation. You must listen.' But he thought he would be in power forever and he tried to take us on the way to Zimbabwe.
"He was a reluctant Head of State, became president for two terms and he wanted to do a third term because a cockroach licking palm oil would never lick enough."
Oshiomole said Obasanjo arrested him because he believed he was trying to overthrow his government.
Oshiomole is an aspirant for the position of national chairman of the All Progressives' Congress (APC) and received public endorsement from the party's national leader, Bola Tinubu, on Tuesday.
Kebbi State governor, Atiku Bagudu, also said all the other governors with the party are backing him to become the APC's new chairman with the tenure of John Odigie-Oyegun set to end.