"I received a report from security last night that certain elements with bad intentions were lurking in the Ciwidey area [west Java] to do something against me," Yudhoyono was quoted as saying by the Antara state news agency.
Dozens of suspects linked to the group have been arrested or killed in recent months.
Rumors have circulated for weeks that Bashir, a fiery preacher known for propagating hatred against foreigners, was next on the list.
Intelligence agencies and the United Nations claim Bashir is the spiritual head of Jemaah Islamiyah, the al Qaeda-linked group responsible for the 2002 Bali bombings that killed 202 people, many of them foreign tourists.
He spent several years in prison for his involvement with the group, but was released in 2006.
Bashir denies connections with Jemaah Islamiyah or terrorism stating he does not believe Jemaah Islamiyah exists.
The preacher's son, Abdul Rohim, insisted his father, who went to Ciamis for a preaching engagement, was innocent.
"He was heading back to Solo when police arrested him together with my mother," he said. "We appeal police to treat my parents well. ... He is innocent, he was just carrying out his obligations as a Muslim."