RIT Capital Partners, chaired by financier Jacob Rothschild, said on Tuesday that discussions over a £5 billion merger are at a "preliminary stage".
Alliance's stock was up 18.5p to 527p after RIT said: "The possibility of combining the two companies for the benefit of both sets of shareholders is at a very preliminary stage of consideration.
"Further analysis and discussion will determine whether such an outcome is indeed in the best interests of shareholders and can be achieved."
Shares in RIT fell 1.43% to 1,595p.
For its part, Dundee-based Alliance said "no detailed terms have been provided by RIT" and have advised shareholders to await the outcome of an ongoing strategic review of the company.
Alliance has been dogged by shareholder unrest, with investors criticising the performance of the 128-year-old investment company. Alliance manages £2.7 billion of assets while RIT Capital Partners manages about £2.4 billion.
Lord Rothschild and other members of the Rothschild family own 21% of RIT's shares.