Bioinformatics is still rather open to people with various backgrounds - biologists, mathematicians, statisticians, physicists, computer scientists. Solid base in math and/or software development is greatly appreciated.
The usual entry paths are:
- Doing Masters in bioinformatics after having done previous studies in another field (usually biologists learn a bit of math and programming, while computer scientists learn a bit biology)
- Doing a PhD in bioinformatics - this seems to be your case. So it may be a good thing to contact potential supervisors for doing a thesis in bioinformatics.
- Doing a postdoc in bioinformatics (similar to the previous option, but later in the career and with less opportunities outside of the academia).
Remark: In English-speaking academia one more frequently talks about Computational biology rather than bioinformatics - it is a broader term, encompassing many useful areas of research (see this thread). It has however limited use outside of academia or in other languages.