The 23-year-old striker joined the Hammers after failing to find his feet at parent club Liverpool but the terms of the agreement have been described as "confidential", with speculation growing that the Anfield club could recall him in January after failing to bring in a replacement on transfer deadline day.
Carroll got off to a flying start for his new team, proving a constant threat to the Fulham defence in West Ham's 3-0 win over Fulham on Saturday before being withdrawn with a hamstring injury.
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Carroll was linked with a move to former club Newcastle throughout the summer but, with West Ham stealing in in the late stages of the transfer window, the London side could be looking to strike a permanent deal with Liverpool to keep the England international at Upton Park after his loan deal expires.