The stock soared 8.16 per cent to close at Rs 93.45 on BSE after it had hit its 52-week high of Rs 95.10.
On NSE, it rose 8.33 per cent to Rs 93.55, which had also scaled a 52-week high at Rs 95.10.
According to reports, the government is in discussion with IFC, an arm of the World Bank, to offload some stake in the public sector entity.
At present, the government holds 76.5 per cent in IDBI Bank, which is grappling with high bad loans and other legacy issues.
"We will consider transforming IDBI Bank in a manner similar to the way Axis Bank was done," Sinha had earlier told reporters.
On Friday, the bank saw a one-day employees' strike, with staff unions protesting against the government's plan to dilute its stake.