The brothers, whose business empire includes bus firm McGill's, invested in the club last year and are in line to buy former chief executive Charles Green's shares when he is free to sell them under stock exchange rules.
In a joint interview with BBC Scotland, Sandy Easdale said: "We took a decision to invest in the club. It is very hard to comment but we are serious about taking it forward.
"We have a delicate deal that when shares are available, we will purchase them. Other shares are an option to us and that is growing stronger.
"Every day we have some more negotiations with other parties."
And the pair confirmed they would expect a formal presence in the management of the club without immediately seeking "complete control".
James Easdale said: "When you spend that amount of money on any business you wouldn't go without a voice. A presence on the board is something we would be seeking in the mid-term."