This seems to be related:

http://www.eurekalert.org/pub_releases/2013-07/afps-iss071513.php

http://www.eurekalert.org/pub_releases/2011-08/afps-sau081611.php

http://knightlab.berkeley.edu/publications/detail/513/

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0008622

http://www.eurekalert.org/pub_releases/2010-01/cmu-cms011210.php

Regards,

Joachim

This seems to be related:

http://www.eurekalert.org/pub_releases/2013-07/afps-iss071513.php

http://www.eurekalert.org/pub_releases/2011-08/afps-sau081611.php

http://knightlab.berkeley.edu/publications/detail/513/

http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0008622

http://www.eurekalert.org/pub_releases/2010-01/cmu-cms011210.php

Regards,

Joachim

What a fascinating question. A bird model might be suitable for the study of the mechanisms underlying inner speech, or "inner song." The zebra finch in particular would be a good model. I recommend looking at the work of Ofer Tchernikovski. He looks at song development and translates his work to human speech development. Your question looks at the other side to speech development. Potentially you could employ a bird model with cognitive tools to measure neural correlates that underlie inner song. Best of luck with your research.

There is quite a lot of old Soviet work.  See Luria's works.

See Peter turkeltaub's recent work on inner speech in aphasia.

A couple of recent articles from 'New Scienitist' magazine:

http://www.newscientist.com/article/mg21829192.300-the-voices-within-the-power-of-talking-to-yourself.html?full=true

http://www.newscientist.com/article/mg22429934.000-brain-decoder-can-eavesdrop-on-your-inner-voice.html

It might not be the exact topic you're looking for, but there are a few researches on subvocalization which might be of interest or at least provide some inspiration: http://www.ncbi.nlm.nih.gov/pubmed/?term=subvocalization

Thank you all for your elaborate answers, really useful! 

There has been quite a bit of work on Trains of Thought especially with regards to mind wandering, but I am not sure that they have tried to capture the internal speech.