WASHINGTON—The No. 2 slot at the Environmental Protection Agency will likely be filled by either a veteran fossil-fuel lobbyist in Washington or a state regulator, reflecting President Donald Trump’s sometimes-conflicting desire to tap industry-backed officials and those outside Washington.

The frontrunners for deputy EPA administrator are Andrew Wheeler, a former top aide to Sen. James Inhofe (R., Okla.) and a current lobbyist representing fossil-fuel companies, and Donald van der Vaart, secretary of the environment for North Carolina under former Republican Gov. Pat McCrory, according to multiple people close to the Trump administration.

The Senate has not confirmed Mr. Trump’s pick to head the EPA, Oklahoma Attorney General Scott Pruitt, so any official announcements for the number-two spot, which the Senate must also vote to confirm, will not come until after Mr. Pruitt is officially at the agency.

Though Mr. Pruitt is likely to win confirmation, given Republicans’ 52-48 Senate majority, the process may take a couple of weeks due to Democrats’ strong opposition. Critics say Mr. Pruitt has been far too close to the oil and gas industry in Oklahoma, while supporters say his experience has given him invaluable knowledge of those affected by environmental regulations.

Both Messrs. Wheeler and van der Vaart have met with Mr. Pruitt about the deputy position, according to people close to the transition effort at the agency.