The bid was submitted by private equity firm EQT and it valued Iress, which is based in Australia, at A$14.80 (£7.80) per share.
This would value the whole company at A$2.86bn (£1.51bn).
Iress, whose XPlan back office software is used by advice firms such as Succession and Ovation, said this offer was not considered to be in the best interests of shareholders.
In a statement, it said: "Following careful consideration, including obtaining advice from its financial and legal advisers, the Iress board unanimously concluded that the indicative proposal was conditional and did not represent compelling value for Iress shareholders.
"The board informed EQT that it was prepared to provide it with access to limited non-public information so EQT can develop a proposal that is capable of being recommended to shareholders.
"This information has been shared with EQT following EQT entering into a confidentiality and standstill agreement. Discussions are continuing."
Iress said there could be no certainty the discussions would lead to another offer from EQT.
There has been an increased level acquisition activity in the adviser tech space in recent months.
Earlier this year FE bought cashflow planning provider CashCalc and Californian software provider AssetMark bought financial planning software provider Voyant.