City A.M. understands Tyrie will publish letters to the bosses of Royal Bank of Scotland and HSBC tomorrow morning.
Tyrie has also written to the heads of the financial regulators the Financial Conduct Authority and the Prudential Regulation Authority requesting assurances high street banks are working to strengthen the resilience and security of their ageing IT systems.
Just yesterday, IT systems for RBS-owned NatWest temporarily went down, causing payments chaos for thousands of its customers.
Problems for the bank left millions of customers unable to access their funds because of a system failure in early 2015.
IT issues have caused problems for Royal Bank of Scotland beyond payments. Sales talks for its Williams and Glyn unit have been repeatedly derailed due to uncertainty over whether the bank will be able to separate its IT infrastructure.
RBS has been instructed to divest of Williams & Glyn by the end of 2017 as part of its £45bn state bailout deal. However, the bank warned in April it might not be able to make this deadline.
It's not the first time the TSC chairman has sought answers on the issue.
Earlier this year Tyrie ordered banks to fix their technology and add better IT expertise to their boards after a series of failures and glitches.