Caledonian Stadium only has 2300 seats
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Dundee United and Dunfermline will put forward a resolution to the SPL which would allow Inverness to play at home.
Inverness were earlier denied promotion by a SPL vote, which was based on them ground-sharing with Aberdeen.
United chairman Eddie Thompson said: "We have now firmly come to the conclusion that Inverness should be allowed promotion to the SPL.
"We are also of the opinion that ICT should be allowed a waiver to enable them to play in Inverness."
The Caledonian Stadium only has 2300 seats, with room for 4000 standing, while SPL rules call for 10000 seats.
And the issue of Inverness playing on home soil has been tabled before and dismissed by the 12 top flight sides.
"Similar proposals have been considered by the SPL at meetings on 30 March and 1 June," said a league spokesman.
"These proposals were rejected by the clubs at these meetings."
However, with two clubs behind the proposal, the subject will once again be discussed.
"We believe that football clubs hold a special position within their own local community and play an important and integral part of that community," added Thompson.
"This community role is severely undermined by supporters having to travel a 200 mile round trip to support their club."
The First Division champions originally failed to gain the eight votes required from the top flight sides for their promotion to be confirmed.
The uproar caused by the rejection, saw Hibs and Hearts table a motion for another meeting and vote - scheduled for 22 June.
Peter Marr is in favour of Caley Thistle being promoted
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Partick Thistle, whose SPL status was saved by the original vote, plan to take legal action if a second ballot goes in Caley Thistle's favour.
The Firhill side said they would accept relegation in exchange for a £1m compensation pay-off but have since withdrawn that offer.
With Livingston and Dundee on record saying they intend to side with Inverness after initial objections, promotion for the Highlanders looks assured.
But just where they will play is unclear.
Dundee chief executive Peter Marr is also in favour of ditching the ground-sharing requirement, which would see Aberdeen benefit by some £600,000 in rental costs.
"We are left with the situation where there's only one resolution on the table, so Caley are going to have to be moved to Aberdeen to let them come up, it's ridiculous," said Marr on Tuesday.
"We support promotion and relegation. You have got to look after the welfare of the spectators and anyone who has been along that road (the A96), and I have, will know it is a horrible journey."
Meanwhile, Clyde, who finished second behind Inverness in the First Division, have made representations to the Scottish Football League about expanding the top flight to 14 or 16 teams.