Saints fans believed the sacking of Nigel Adkins in January was harsh and largely unjustified for a manager who looked on course to steer the south coast club to safety, but Pochettino has overseen an impressive run of form since he took charge.
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He told reporters:"In the next two years I want to be back in the Champions League with Southampton and I believe it’s not unreal.
"We are a well organised side, with great belief in our abilities and it’s not an accident that we have beaten Chelsea, Liverpool and Manchester City recently."
When quizzed on whether it will take time to get to that level, Pochettino said: "Why in a couple of years? It might be next year. I think in football if you have to be something, you have to be optimistic - why not dream of big achievements, big goals?
"We are an ambitious club and we have a clear way of how we want to proceed and the type of football we want to be playing, where there are means of getting that done.
"Why not put in the effort, the imagination to make that happen and dream together to reach for the stars, why not?"
Although Pochettino is looking ahead of the end of this season, the former Espanyol manager is eager for his side to finish well, starting with West Brom's trip to St Mary's on Saturday.
"It is really important for us finish the season well," he said. "We have to get the maximum number of points out of the games we have left, starting on Saturday.
"We know that the game against West Brom will be a tough one, we know they are a good side but at the same time we are on a good run of games.
"As I have said before, every game in the Premier League is a tough one and all of our rivals are tough to play against so we have to focus on Saturday to get a good result and continue the run."
Pochettino is already thinking of the players he will require for his mission next season, but insists he will only add players that can improve the overall quality of the squad.
"I think there is already a good level of quality of footballers in my squad," he added.
"But we are open as a club to try and reinforce in the positions we feel we need to improve - logically if we have the chance to improve then of course we will go for those players and I'm sure that my squad and the club itself would welcome new signings."