Jesse Norman, fellow Conservative and former Barclays banker, is believed to be seeking the role for the coming parliament.
Such a move could shock political and financial circles, given that Tyrie is held in high regard. When parliament reconvenes, all MPs vote on the chairmen of the select committees. Tyrie has headed the influential backbench committee since 2010, and built a name for himself as an insightful and effective leader, scrutinising Treasury and Bank of England officials, as well as bankers and other financiers.
His style was also praised as serious and even-handed, compared with chairmen of other committees who often use the position as a soap box to bash political opponents. Tyrie also headed the Parliamentary Commission on Banking Standards, which contributed to a series of banking regulations.
Norman has also made a name for himself, sitting on the TSC since 2010 and using his experience of financial services to scrutinise regulation and private sector witnesses.
Both Norman and Tyrie were unavailable for comment.