Chief executive Antonio Horta-Osorio and chairman Sir Win Bischoff have been summoned to appear before the Treasury Select Committee next week as part of an inquiry into the failure of the deal thought to be worth £750 million.
Co-op pulled out of the branch takeover in April over fears about the strength of its banking arm's balance sheet, shortly before ratings agency Moody's downgraded it to junk status and warned it may need taxpayer support.
The deal would have transformed Co-op Bank into a major customer-owned rival to the big four high street banks, creating a lender with almost 1,000 branches and 11 million customers.
Lloyds, which has to divest the branches as an EU condition of state aid, will instead float the branches on the stock market under the TSB Bank brand.
The deal's demise has given the Government a major headache with its plans to increase banking diversity, particularly in light of Royal Bank of Scotland's failure to sell 316 branches to Santander.
"We will want to know how The Co-operative Bank's bid was allowed to progress to such an advanced stage, why it collapsed and what will now happen to these branches and their customers."
It is thought that the Lloyds chiefs will also be questioned about whether there was any political pressure for them to originally choose the Co-op's bid over rival groups such as investment firm NBNK.
Former Co-op Group chief executive Peter Marks reportedly may also be called up before the committee.