The Mirror says the Argentina goalkeeper wanted to join Manchester United and even informed Villa of his wish.
However, United decided against signing Martinez and instead went with the younger option, Senne Lammens, who signed from Royal Antwerp on Monday.
Martinez, meanwhile, has managed just the one appearance for Villa, with confidence growing that Marco Bizot can handle being the club's No1.
Indeed, heading into Monday's deadline day, Villa boss Unai Emery said: "We need players who are focused, 100%. He wasn't. It's not helping us. It’s one of the circumstances that we are having now not helping.
"Tomorrow the window finishes and we are expecting something to improve our squad. Keep calm. One of the circumstances is Emi Martinez, we will see tomorrow and then we try get the balance and work after the break."