Even though Android uses a Linux kernel, the operating system itself cannot actually run standard Linux applications, and Android applications can't run on a standard Linux distribution. The cause of this is that Android uses a custom Google Java runtime for its applications, with no tools or support for regular Linux applications. In addition, since this Java runtime is very customised, Anroid applications cannot run in normal Java environments.
The Canonical team is working on allowing Android applications to run on regular Ubuntu. To achieve this, they've built a prototype execution environment which already compiles against Ubuntu's libc instead of Android's custom variant, and runs on top of a standard Linux kernel. In addition, they're working on a special kernel driver which will allow Binder, Android's IPC system, to run properly. This driver is in the kernel staging area and not enabled; they're using workarounds for now, but they hope the driver will be part of the kernel before the next Ubuntu release. In addition, they are working on a "compatibility shim", which will allow the Android applications to see the filesystem and to take advantage of other system services. Part of this shim is already implemented in a library called Libwrap.
For now, it's all highly experimental, and the code isn't even out there yet; they plan on releasing the code soon.