Scottish Hydro-Electric Transmission Ltd, a division of energy giant SSE, submitted the "needs case" as part of the planning process for the cable.
After assessing the case, energy regulator Ofgem has asked for further details to be submitted.
The project has been hit by delays and a rise in costs to an estimated Â£780m.
Islands local authority, Comhairle nan Eilean Siar, has said major renewable energy projects planned for the isles cannot go ahead without the cable.
The interconnector would export electricity to the mainland for distribution.
It would stretch to about 50 miles (80km) from Gravir on Lewis to Ullapool on the north-west coast of mainland Scotland.
The Scottish government has been involved in talks on the project.
A spokesperson said: "This is a matter for SSE and Ofgem, but we would encourage the company and regulator to move swiftly to resolve this issue.
"Improved grid connections will enable the huge renewable energy resources of Scotland's islands to create jobs - up to 3,500 jobs in the Western Isles, almost 2,900 in the Shetlands and over 4,500 in the Orkney Islands by 2030.
The spokesperson added: "SSE put a business case for the Western Isles link to the electricity regulator Ofgem on 14 June, and today Ofgem have responded by setting out the detailed further information they require."
Ofgem has asked for more information on why a subsea cable is needed to carry electricity generated on the Western Isles to the mainland.