Ms. Lake, an ally of former President Donald Trump, has said she is focused on her election lawsuits, but aides say she is considering entering the race for Senate. Her entrance would add further unpredictability to what could be a three-way contest for the seat currently held by independent Sen. Kyrsten Sinema. Republicans see the seat as a prime pickup opportunity as they try to win back the Senate.

Ms. Lake, a charismatic former local TV anchor, narrowly lost the contest for governor by 17,000 votes in November's midterm elections. She was one of several Republican candidates across the country who aligned themselves with Mr. Trump and his false claims of election fraud and lost in competitive states. A fresh Lake candidacy would test anew how Arizona voters feel about the former president and his aggressive political style in a major battleground.