You may use yii\mongodb\i18n\MongoDbMessageSource for the i18n message translations storage. Application configuration example:
return [
//....
'components' => [
// ...
'i18n' => [
'translations' => [
'*' => [
'class' => 'yii\mongodb\i18n\MongoDbMessageSource'
]
]
],
]
];
Please refer to yii\mongodb\i18n\MongoDbMessageSource for more details about configuration and translation collection data structure.