A senior official confirmed the proposed move, which is expected to be ratified by the Senate. The president's office could not be reached for comment.
Espinosa has been the treasurer at the finance ministry since 2009, and would fill the vacancy left by newly installed Banco de Mexico Governor Alejandro Diaz de Leon, a former deputy governor who took over the top job at the bank late last year, replacing Agustin Carstens.
The five-person central bank board is responsible for setting interest rates, which are currently at 7.25 percent, their highest level in nearly nine years.
Mexico's annual inflation rate climbed to a 16-1/2-year high in 2017, data earlier this month showed, piling pressure on the central bank and its new governor to act again next month to rein in inflation after raising borrowing costs at the December monetary policy meeting.
Espinosa taught at Mexico's ITAM University, a cradle for many of the country's top economic policymakers, between 1997 and 2000, and has also worked at the Inter-American Development Bank.