You can use ChIP-seq.

For this, you need  specific (pimary) antibody against your protein and some antibody which is specific against your primary antibody. That way you can use ChIP to isolate the Specicfic DNA fragment which you can sequence using next generation sequencing.

Take a look at the article below to get an idea of what I am saying

Tran, V., Gan, Q., Chen, X. Chromatin Immunoprecipitation (ChIP) using Drosophila tissue. J. Vis. Exp. (61), e3745, doi:10.3791/3745 (2012).

You can try to scan your DNA sequence with motif finding tools like TRAP algorithm (http://trap.molgen.mpg.de/). In parallel you can align your AA sequence to verify if exists an homology with known transcription factors. The intersection between the results of these two analysis will give you some low cost clues.

Thanks a lot for your suggestions