The proposal would see £3.7m due to Milne and £2.25m owed to Aberdeen Asset Management turned into shares, cutting the club's debt to £10.82m.
Shareholders will be asked to vote on the matter at the club's AGM On Wednesday, December 19.
"Over the past few years the major shareholders have invested substantially in the club, with interest free loans now standing at £5.75m in aggregate," Milne said in a statement.
"Part of this amount has been used to finance the development costs of the new stadium and part to provide finance for the business.
"The major shareholders now wish to make this investment in the business permanent and to this end, and subject to shareholder approval, it is proposed to convert the loans over time into a new class of preference shares.
"After the ordinary business of AGM, shareholders will be asked to vote on a special resolution which would create this new class of share.
"No new cash will come into the company as a result of this conversion but over time its financial position will be considerably improved by removing liabilities from its balance sheet totalling £5.75m and by the corresponding improvement in the ratio of its net assets to called up share capital."
Earlier Aberdeen announced trading results for the year until June 30, 2012 where turnover rose from £7.462m to £8.337m and operating loss fell from £589,000 to £334,000.
On moving away from Pittodrie, Milne added: "Preparations for the move to a new stadium at Loirston received a set-back when Aberdeen City Council rejected a request for an extension of time to conclude an agreement in relation to the Calder Park development.
"We continue to investigate options for Loirston and alternative sites with a number of interested parties and remain confident a satisfactory solution will be found in due course."