Linux requires a Memory Management Unit (MMU). There is a variant of Linux that works around the MMU requirement and is targetted to the embedded microcontroller market. This "lighter" version of Linux is called uClinux.

Embedded Linux/Microcontroller Project
http://www.uclinux.org/

Though it's probably possible to make uClinux work on an 8051 with enough effort, it's probably easier and more cost effective to use a 32-bit processor.

For example, we've ported uClinux to run on our ARM7TDMI-based A7 devices.