Halliday & Matthiessen (1999: 115):
Quoted offers naturally retain the property of being variously realised in the mood system:declarative: She said: "I can do the laundry."interrogative: She said: "Shall I do the laundry?"imperative: She said: "Let me do the laundry!"However, reported offers can always be realised in the same way as reported commands — as in the case of reported propositions, the distinction in orientation between giving and demanding is realised by the projecting clause; for example:command: she told him —> to do the laundryoffer: she offered (promised; threatened) —> to do the laundryThe category ofreportedprojected proposal is thus realised generally as a perfective non-finite clause when it is reported.