On 14 August 2016, Moreno started in the first game of the season, a 4–3 win at Arsenal, where he conceded a penalty and was criticised heavily for his performance, prompting a defence from his manager Jürgen Klopp. Despite his manager's intervention, he was dropped and used only as a late substitute for the next game, an 0–2 loss at Burnley. He made 18 appearances over the season, just eight as a starter, as James Milner was preferred in the left-back slot.
Moreno has many tattoos. In April 2016, he had his leg decorated with an image of a gun-toting chimpanzee dressed in a suit and wearing headphones; ESPN FC's verdict was "Please don't ask, because we haven't got the slightest clue." The back of his leg is decorated with the coordinates of his hometown's Plaza de España. Moreno has two children with his partner Lilia Granadilla.