The Barclays Premier League clash at St Mary's comes between the two legs of City's Champions League semi-final against Real Madrid, which is delicately poised after Tuesday's goalless first meeting at the Etihad Stadium.
Excitement is inevitably building ahead of Wednesday's return at the Bernabeu but City can ill afford to take their eyes off domestic matters, as their place in next season's Champions League is not secured.
City are third in the table heading into this weekend's fixtures but only five points ahead of fifth-placed Manchester United, who have a game in hand.
Pellegrini wants to see the same level of commitment that saw his side win their league games ahead of both quarter-final legs against Paris Saint-Germain and then thrash Stoke last weekend.
The Chilean said: "It was difficult when we played Paris Saint-Germain with Bournemouth and West Brom, and when we played last Saturday before Real Madrid, but we have two different competitions.
"I always say if you want to be involved in all the competitions you have to have a strong squad, not just in the team with 11 players.
"I think it is very important to have an ambitious and winning mind
That is why we always demand the best performance of all our players.
"In this moment we want to win the last three games of the Premier League and are involved in the semi-finals of the Champions League
I trust all of them and we will see which is the best starting XI for Sunday.
"We want to be as near to the top of the table as we can and it is very important for this club to continue (being) in the Champions League."
A poor winter spell aside, Southampton have enjoyed another impressive season and, with European qualification still a possibility, they are unlikely to be easing up.
Ronald Koeman's men have lost only to leaders Leicester in their last seven games and Pellegrini has been impressed by Saints under their past two managers.
Pellegrini said: "Southampton is not only Ronald Koeman, but with (Mauricio) Pochettino also
For the last three or four years they have been doing very well
They have very good players.
"They sold a lot of players, so that is the merit of Ronald Koeman, to keep the team in a good position
I think they are a team that plays football."
City are without playmaker David Silva, who suffered a hamstring in the first leg against Real and will also miss the game in Spain
Yaya Toure also remains on the sidelines with a thigh injury but is pushing to be involved at the Bernabeu.
Samir Nasri is fit again after a muscle problem and Raheem Sterling could get more game time as he continues his return from a groin injury.
Pellegrini said: "Raheem had a difficult muscle injury for around one month
Kevin De Bruyne returned very well with his best performance so I hope that Raheem will do the same thing."
Source : PA
Source: PA