REUTERS/Jim Urquhart
Mitt Romney in Utah in March.
The former Massachusetts governor ran for president in 2012, but lost to President Barack Obama.
Romney and Trump reportedly plan to meet this weekend to talk about the State Department job.
Romney was one of Trump's most vehement critics during the Republican primary, speaking out against him frequently and refusing to give him an endorsement.
Trump is also considering several other people for secretary of state.
Romney's spokesperson did not immediately respond to a request for comment.