LM358 saturates the output

Yoram:
I am not worried about the output dc voltage, I know I can remove it with a cap. The problem is that I am not able to locate this dc level consistently at say vcc/2 (or (vcc-1.5)/2) so that I can get the max swing without saturation...

That's ok. I was just responding to your comment you made below, where it appears that you assumed that the output DC level should be zero.

Yoram:
Still the output DC voltage at zero input is not zero and can be something like 2-3V. ???.

To get the output DC voltage roughly to be at Vcc/2 ..... you could :

option a) use the 7.5 V source, and use two of the same resistors eg ... 10K and 10K to make a voltage divider.... which will be used to set the + terminal to 3.75V

option b) use the 5 V source, and use an appropriate voltage divider to set the + terminal to around 3.75 V.... such as a 33K resistor and a 100K resistor divider.

Your diagram has a 7.5 V source, which will be Vcc. And your diagram also has a 5 V source, which is where you could use the 33K and 100K divider.

And, finally, you won't get saturation if you decrease the gain of amplifier (by, for example, by replacing the 75K resistor with a smaller one)..... or if you use smaller AC input values.