Republican Sen. Kay Bailey Hutchison is retiring from the seat.
"Gen. Sanchez has spent his entire life serving our country, and there's no question he would be a strong candidate," Matt Canter, spokesman for the Democratic Senatorial Campaign Committee, said in a statement reported by Politico.
In an interview with McClatchy Newspapers, which broke the story of his possible run Friday, Sanchez did not confirm his interest but said, "Socially, I'm a progressive, a fiscal conservative and a strong supporter, obviously, of national defense. … It's my views and my history, having grown up in South Texas, depending on social programs and assistance, that America has a responsibility to its people."
CBS reported Monday the campaign committee expects him to run.
"He's the one guy who could unite the Hispanic vote," Lt. Gov. Ben Barnes said. "He'll get the conservative Hispanic businessman."
The 2010 Census found Texas is now 38 percent Latino.
Sanchez gave up his command in Iraq and retired after the Abu Ghraib scandal in 2004, although he was not implicated in prisoner abuse.