7.50 modals in reported clauses

The basic rules for using modals in reported clauses are as follows.

If the verb in the reporting clause is in a past tense or has 'could' or 'would' as an auxiliary, you usually use 'could', 'might', or 'would' in the reported clause.

If, as is less common, the verb in the reporting clause is in a present tense or has 'can' or 'will' as an auxiliary, you usually use 'can', 'may', or 'will' in the reported clause.