In an apparent about face, Fannie Mae and Freddie Mac’s regulator told congressional Democrats Wednesday that he welcomes their input on coming up with a plan to free the mortgage giants from federal control.

“As we begin the journey of evaluating the enterprises and developing a framework for ending conservatorship, I would welcome your insight and perspective,” Joseph Otting, the acting director of the Federal Housing Finance Agency. wrote in a letter to House Financial Services Committee Chairwoman Maxine Watersand...