There is a project that tries to turn Linux into a library which could lead to a unikernel approach with the Linux. If you look at https://github.com/lkl you can see where they are.

A leaned down Linux-kernel with the application linked into kernel space would be pretty comparable. But it would be pretty enormous beast.

You can compile the Linux kernel with only the modules necessary for running it in a virtualized environment (ie, only virtio modules) and simply include your application in the initramfs as init. If you include nothing else, that's about 6MB + your application.