Perpetual rejected a $A30 per share offer proposal from Barings Private Equity Asia (BPEA), which was recently bought by EQT (EQTAB.ST), and Australian firm Regal Partners (RPL.AX).
Perpetual shares rose by as much as 10.1% early on Thursday, the company's best session in more than two years, before retreating to be up 6.6%.
Perpetual said it would press on with its planned A$2.51 billion acquisition of rival Pendal Group (PDL.AX) announced in August.
The private equity offer represents a premium of about 11.5% to Perpetual's last close of A$26.90.
BPEA is one of the region's largest private equity firms and was bought by EQT in March.