Consumers have reported being told they will receive their pre-ordered iPhone 4 by 4:30 pm on 24 June.
A number of customers have updated their Twitter accounts to say they have received shipment e-mails from Apple, stating the expected delivery date.
Some consumers even claim to have received notification from Apple that their iPhone 4 will be delivered as early as 23 June - a day before the device is due to arrive in retail stores in the United States and the UK.
The reports come amid news that Apple and AT&T have been contacting some customers to say that their iPhone 4 pre-orders have been cancelled, due to incomplete authorisation processes and unverified payment details.
Pre-orders for iPhone have exceeded many retailers' initial estimates, according to Apple and AT&T. It is believed that the unexpected demand may have led to delays in some quarters.
Apple has reported receiving about 600,000 advance orders for the new device.