WASHINGTON — With every new plum job opening in Washington comes a political guessing game: Who is on the president’s shortlist?

Making the list is worth more than just an ego boost.

In January, Politico reported that President Trump was considering Sean Reyes, the Utah attorney general, to lead the Federal Trade Commission. Since then, donations to his political campaign have poured in from out-of-state donors and businesses that are regulated by the F.T.C.

Mr. Reyes, who is not up for re-election and won handily last year, received more than $113,000 in donations in the first three months of the year, far more than he received during the same period last year, an election year. Half of the new contributions came from out-of-state donors, and more than $43,000 came from first-time donors.

There is nothing illegal about the donations, but their timing reveals the power of the political shortlist in a city where lobbyists and businesses often place protective bets. Mr. Reyes, 46, is considered a rising star in the Republican Party.