Foden has 24 goals for City in all competitions this season and has often been utilised in more central roles by coach Pep Guardiola
Reports said Moeen had already informed captain Joe Root and head coach Chris Silverwood.
The 34-year-old has scored 2,914 runs in 64 tests at an average of 28.29 and taken 195 wickets with his off-spin.
Having played little test cricket since the 2019 Ashes, Moeen was recalled for the home summer series against India and played in three matches.
England's next test series is against Australia in the Ashes starting in December.