While United remain unbeaten under caretaker manager Michael Carrick, the board are exploring a long-term appointment. Carrick's deal only runs to June.
Transfer expert Ben Jacobs is reporting Martinez, formerly in charge of Everton and Wigan Athletic, is under consideration.
“One of the names I’ve been told is being considered internally at Manchester United is Roberto Martínez.
"He’s expected to leave the Portuguese national team to make way for José Mourinho, and he’s on the shortlist.
"However, I don’t think Martínez’s style would put him at the top of the list for the job, but he’s definitely on it, along with Nagelsmann and (Roberto) De Zerbi,” Jacobs stated on The United Stand podcast.
Martinez's deal with the Portuguese Federation expires after this year's World Cup.