1) Dominate English football
It remains to be seen how many trophies City will hold when Guardiola takes over, but whatever their success in the remainder of this season, the club will still be hungry for more. They want to become the dominant force in English football.
City may have won two Premier League titles in recent years and another could follow, but they will want to be winning them more convincingly in future. Bayern Munich have dominated in Germany under Guardiola - after a period of Borussia Dortmund success in the not-too-distant past - and City will hope the same blueprint works for them.
2) Champions league progression
City are still relative newcomers to the Champions League scene, but they can no longer use the excuse they are inexperienced on that front. The current campaign is their fifth in the elite competition and they now want to take the step to becoming serious contenders to win it.
Pellegrini could yet take them to the quarter-finals for the first time but City will be expecting this to become the norm from now on.
3) Replace Yaya Toure
Toure has been City's midfield driving force for much of their recent success but there have been signs this season that he could be on the decline. Even if he rouses himself for one last strong push this term, at 32, he is clearly closer to the end of his career than the beginning.
City were told the asking price for Paul Pogba last summer was $150 million-plus, a figure they baulked at. But with Guardiola in charge, money is no longer the only attraction and more glamour signings of his calibre could be possible.
4) Find a reliable central defender
In the past two summers City have spent a combined $155 million on centre-backs Eliaquim Mangala and Nicolas Otamendi but still their defence has frailties and is over-reliant on captain Vincent Kompany. Kompany is a rock when fit, but the team have not seen enough of him this season due to yet more muscle - chiefly calf - injuries. Finding a reliable partner should be a priority.
5) Bring in a new striker
Although Pellegrini has often played with just one central striker, City have still looked a little short on numbers up front. This is because Sergio Aguero and Wilfried Bony have both had injury problems this term, leaving Kelechi Iheanacho as the only out-and-out replacement. Iheanacho took his opportunity well at the weekend - scoring a hat-trick in the FA Cup win at Aston Villa - but City may want more, particularly with Bony's future uncertain.