City crashed out of Europe in a surprise 3-1 loss to Lyon as they were knocked out in the quarter-finals of the competition for a third consecutive season.
Despite winning two Premier League titles and an FA Cup during his four-year spell at the club, spending almost £700 million in the process, Guardiola is yet to win Europe’s top prize.
Toure – who played under the Spaniard at Barcelona and City – believes Guardiola was brought to Manchester to deliver the Champions League, and the fact he hasn’t done so could spark a change at the Etihad.
‘The manager has been signed to bring this trophy,’ Toure told Sky Sports.
‘When you see opponents like Liverpool and other clubs win it without doing a lot of work in the transfer market, it’s quite strange and disappointing.
‘He’s been brought to the club to get massive trophies for them. At the moment it’s not been delivered in the way they want.
‘Everybody knows Pep is a great manager, but at the moment, when things aren’t going their way, sometimes is it time maybe to change? I don’t know, we will see.’
City also have the challenge of winning back their Premier League crown after Liverpool’s league title victory last term.
Guardiola’s side face Aston Villa at the Etihad in their 2020/21 season opener, but, the fixture has been postponed to give them extra time to recover from their European campaign.