Yes you can explore the second opportunity. This is especially true when your current job is in jeopardy.
When the first position makes you a formal offer, they will ask you to drop any other internal positions you are looking at, or any positions you are being considered for, when you accept their offer. They do this because they don't want you to accept the offer, then go with the a second internal position that make an offer the next day.
There is no guarantee that the offer for the first position will be what you want. In the past I have rejected formal offers for various internal transfers because despite what I was told in the application process and the interview:
- the new position was a pay cut;
- the work location was 30 miles away;
- the contract was only good for 60 days;
- I would have to work nights for the first year;
- they would have to wait for the new contract to be awarded in a few months.
Just like applying for external options, you want to keep your options open. Expect that they can see any internal applications, and be honest about them; unless of course your current boss knows nothing about your looking for a new position.