The institute warned it could face significant pressure if such a bank with a stronger credit rating was to arrive, the Irish Independent reports.
According to the Bank of Ireland - a group that first opened its doors at Mary's Abbey, Dublin in 1783 - a takeover of one of its competitors could result in its deposit base and funding being seriously impacted, which might have considerable implications for its shareholders.
In its latest bond prospectus, the bank noted such action could have a notable effect "if a significant number of depositors transferred their deposits from the group to the competitor due to the new owner's stronger credit ratings".
It went on to point out that a new financial body may be able to lend at lower rates as a result of access to cheaper funding.
By Asim Shah