Baring Tribune said it had received an approach from EFM and Edinburgh UK Tracker Trust which "might or might not lead to an offer".
The trust has already been approached by Legal & General and Fleming Claverhouse, and a decision is expected by the end of the month.
Baring Tribune's problems started at the end of last year when the investment trust, which has been trading at a discount to its asset value, was targeted by Advance UK, a vulture fund. After buying up large chunks of Baring Tribune's shares, Advance UK tried to force the investment trust to convert into a unit trust. This would allow shareholders to realise the full value of the underlying assets.
Advance UK's proposals were voted down in a shareholders meeting.