Manohar's elevation to the role follows the Board of Control for Cricket in India's (BCCI) decision to remove Srinivasan as its ICC representative and name the 58-year-old in his place.
Manohar will occupy the position until the end of June 2016.
Indian cricket was hit by a series of corruption scandals last year.
Srinivasan, 70, stood down as BCCI chief after the Supreme Court last year found him guilty of conflict of interest issues regarding his ownership of the Chennai Super Kings team in the Indian Premier League.
Srinivasan's son-in-law, Gurunath Meiyapppan, was found guilty of illegal betting while serving as team principal at Chennai and banned from all cricket-related activities.
An administrator removed by his home board cannot serve in the ICC, but it has yet to confirm Manohar's appointment.
A short statement read: "The ICC notes media reports, but it is yet to receive an official notification from the BCCI regards its decision to change its nominee to the ICC board."
The BCCI has since confirmed its position, stating: "Mr Shashank Manohar will be the BCCI representative at the ICC."
Shashank Manohar is set to replace N Srinivasan as chairman of cricket's world governing body for the remainder of his term.