This link shows what kind of dialog there is:
The issue is that the dialog tells to empty trash and use 'sudo apt-get clean'
which may help only, if /boot is on same partition than some of the files in
trash, the /var/cache/apt/archives/ or /var/cache/apt/archives/partial/.
In Ubuntu 16.04 and later a more helpful advise would be to run "sudo
apt-get autoremove --purge". (That might not do the trick in 14.04 due
to Bug #1439769)
For more control on which kernels to purge, this utility would be
You received this bug notification because you are a member of Ubuntu
Bugs, which is subscribed to Ubuntu.
Software Updater does not guide user to remove excessive kernels when
there is too little space on /boot to install a kernel update.
To manage notifications about this bug go to:
ubuntu-bugs mailing list