The Black Cats have struggled this season and are currently just one point clear of the relegation zone heading into the game at St Mary’s Stadium.
Cuellar feels the game will have huge significance, being against a rival at the foot of the table, but feels he and his team-mates are ready for the challenge.
He told the club’s official website: “I am looking forward to playing there and this is one of the most important games so far this season.
“Southampton are a direct rival for us and we need to win with some other good games coming up. I think the team are ready and mentally strong.”
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The Spaniard insists Sunderland have to repeat their recent second-half performance against Manchester United, that saw the Black Cats put their hosts under sever pressure before succumbing to a 3-1 defeat, but maintain that level of play over a full game.
“The second half against Manchester United – we need to try and find that from the first minute,” he added.
“If we can do that then not many teams will beat us. The other players know that and everyone is ready for this weekend.
“It’s important to start Christmas well. There is a lot of games. We have to be ready for every game and we are looking forward to it.”