Perhaps I'm misunderstanding. It sounds like you're currently in a contract with your current employer.
You should be looking for your next job after that, and they should expect that of you (although from what I understand many poorly run companies don't understand this).
Your manager understandably feels concerned about your leaving. If you leave before the job is done, it will impact him (e.g. he didn't complete the project on time).
First, make it clear to your manager that you are happy with your current job, will absolutely honor your commitment, like him, like the company, etc. Don't add to his concerns, and at this point alleviate them. That said, explain that you have to be concerned about your next project (again note that you will not leave before this job is complete). This could be a good way to nudge him about extending your contract. To do that, for example, you could note how much you like this contract, and that you felt anxious because they haven't talked about renewing it. At this point he might work to lock you in by extending your contract (note: don't think you've got it until you have a signed contract and one they can't reneg on without penalty; some bad employers will simply
string you along until the other role is filled.)
--Mark