The Reds defender has stayed with his club side during the international break after Moreno missed Liverpool’s latest Premier League game due to an injury problem.
Daniel Sturridge and Philippe Coutinho gave the Reds a 2-0 lead at St Mary’s, but Southampton emerged as 3-2 winners thanks to goals from Sadio Mane and Graziano Pelle.
Moreno watched the league game from the comfort of his sitting room after he limped off during Liverpool’s 1-1 draw with Manchester United last week.
The former Sevilla defender was adjudged to have suffered a hamstring injury but his presence on Liverpool’s trip to Tenerife suggests that Moreno could make a swift return to training.
Liverpool will host title hopefuls Tottenham Hotspur in their next Premier League game at Anfield on Saturday 2 April.
MORE: The latest football news