The short answer is no.

Basically, you would need LOTS more ram then even the biggest ATmega has natively.

It is theoretically possible to add external hardware, and program the ATmega to emulate a more powerful CPU, and run linux on that. However, on a plain arduino, it is not possible.

It would be much more realistic to run linux on a Arduino Due, which is basically a AT91SAM3X8E CPU. However, you'd still need to add some additional SRAM and storage.

There are things like the Arduino Yun, but that is really a entirely separate linux module on the same PCB as a ATmega32U4, so I don't know if you can really count it as an arduino.

Possibly relevant: What does it take to run embedded linux?