The deal would only go ahead if Zurich felt it was getting a fair deal, said chief executive Martin Senn.
His comments came as Zurich reported a 1% dip in net profits for the April to June quarter to $840m (Â£538m).
Separately, RSA reported pre-tax profits of Â£288m for the first half of 2015, beating analysts' estimates and dwarfing 2014's results.
RSA is amid a turnaround process under chief executive Stephen Hester.
The firm said it planned to have "substantially completed" that process by the end of the year.
Last month, Zurich said it was considering a bid for RSA, the owner of the More Than brand, which has a market value of about Â£5.3bn.
Zurich is Europe's third-largest insurer and has often been linked with a bid for RSA.
The Swiss firm said that its second quarter results were hit by "large losses" in the UK and at its global corporate business in North America, and "higher levels of catastrophe and weather related losses".
The head of Swiss insurer Zurich has said he sees "significant benefits" in buying UK rival and bid target RSA.