According to The Athletic's David Ornstein (h/t the Mirror's Darren Wells), although it's said the Catalan coach is set to see out his deal and could even extend it, the club are making preparations for a departure as early as the end of this season.
Guardiola will have been at City for four campaigns by then; he has never stayed in a managerial role at a club beyond that.
In case of an early exit, City have already begun searching for a new member of the backroom staff to work alongside the first team's medical and fitness departments.
It is said the role would become much more involved should the coach move on, and potential recruits have been informed that this could be a possibility at the end of the season.
Fox Sports' James Dodd suggested Guardiola's days at the Etihad could be numbered after City's 2-1 defeat to Manchester United on Saturday:
The 48-year-old spent four seasons in charge of Barcelona from 2008 until 2012. In that time, the club won three La Liga titles, as well as the UEFA Champions League and the Copa del Rey twice apiece, among other honours.
He then spent a year on sabbatical before taking charge of Bayern Munich in 2013. They won three Bundesliga titles and two DFB-Pokals before he swapped Munich for Manchester in 2016.
City finished third in the Premier League—having collected 12 more points than they did in Manuel Pellegrini's final year in charge—and without silverware in Guardiola's first campaign.
The Sky Blues collected a record 100 points in his second season as well as winning the Carabao Cup. Last season, they won the league with 98 points as part of a domestic treble alongside the Carabao Cup and FA Cup.
City have struggled under Guardiola this season, though, and find themselves 14 points behind Liverpool in the title race.
The manager has suggested they're no longer able to compete at the top level:
Guardiola: "Man Utd have the quality to defend and the quality to attack on the counter-attack. That's the level we face against Liverpool, Man Utd, Barcelona, Real, Juventus. They're the teams we have to face and the reality is maybe we are not able now to compete with them." 😲 https://t.co/sPmzTjX921
It is perhaps no coincidence that the Citizens have struggled following the departure of club captain Vincent Kompany in the summer. The Belgian had been a leader and a talisman for the team since he joined in 2008.
City could be set for further difficulties next season as two other stalwarts, David Silva and Fernandinho, are in the final year of their contracts.
Guardiola leaving at the same time would be disastrous, so it's a wise move for them to prepare as best they can if they find themselves needing to transition to a new coach earlier than expected.