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."

Spireites midfielder Gary Liddle was sent off after only 16 minutes for a foul on Kane Vincent-Young.
Chesterfield kept the U's out until Drew Wright broke free with 20 minutes remaining, cutting the ball back for Bonne to strike right-footed.
However, three minutes later Lee Novak converted from the spot after he was felled by Richard Brindley.
Colchester's winless run in League One stretched to 17 matches as they remain rooted to the foot of the table while a point was enough to take Chesterfield out of the relegation places.

Morgan-Smith was available on a free transfer after he was released by the Latics, having made only four starts for the League One club this season.
The 26-year-old has previously had spells with Stockport County, Luton, Macclesfield and Kidderminster.
"I want to try and get this club back into the Football League where they should be," he told the club's website.
Ofgem has asked for more information on why a subsea cable is needed to carry electricity generated on the Western Isles to the mainland.
[NEXT_CONCEPT]
Macauley Bonne scored his first goal in 11 games but Colchester were held to a draw by 10-man Chesterfield.
[NEXT_CONCEPT]
Relegated Cheltenham Town have signed former Oldham striker Amari Morgan-Smith on a one-year deal.