Sky News has learnt that Mr Sharma has picked Jonathan Scott, a board member at the Competition and Markets Authority (CMA) since 2016, to replace Lord Tyrie on a temporary basis.
An announcement, which is expected on Tuesday, will underline ministers' desire to address the leadership vacuum at the UK's principal competition regulator more than two months after the former Conservative MP was effectively forced to step down.
Lord Tyrie left the CMA three years early after becoming involved in a stand-off with Andrea Coscelli, its chief executive, over the chairman's leadership of the organisation.
Mr Coscelli is said to have indicated that he would resign if Lord Tyrie, a respected former chairman of the Treasury Select Committee, did not stand down.
Mr Sharma's decision to name Mr Scott as interim chair of the CMA will install an experienced corporate lawyer in the post, although it was unclear on Monday whether he was a candidate to be the long-term successor.
Mr Scott headed the competition practice of Herbert Smith, the City law firm, for more than a decade, and went on to become senior partner and chair of its successor firm, Herbert Smith Freehills.
His appointment will come amid questions about the future of Britain's state aid regime, which is unlikely to be finalised until well into 2021.
On Monday, the Department for Business, Energy and Industrial Strategy announced that John Penrose, a former Tory minister, would oversee a review of UK competition policy.
"Competition drives down prices, creates a wider choice for consumers and leads to better quality products and services," Mr Sharma said.
"This review will ensure the UK's competition regime is in the strongest possible position as we build back better from the pandemic and start our fresh new start outside of the EU - delivering for businesses and consumers in every corner of the UK."
BEIS declined to comment on Monday on Mr Scott's appointment.