Is she not interested? Something is definitely fishy. What do you suggest?

I turned 27 recently and now I have a good job so I thought of planning to marry and suddenly I got to know that a girl who is 2 years elder to me is also looking for a groom. I took this opportunity but she wanted to keep it between us and I was fine as when families get involved matters become too serious.
But she tells me she doesn't talk much, she gives too late replies and then tells me "sorry for replying late, I was busy with something" its been a story of 10 days now. Moreover she just replies to my questions. It isn't a conversation, its just a one sided answering of my curiosity to know her. She hardly asked me 5 questions in the past 10 days.

I feel sad that her friends asked me if I was interested to talk to this girl who is also looking for a partner and still she isn't taking initiatives to talk. I tried this yesterday: If I say Good morning, she will just reply good morning and thats it end of conversation. She just doesn't talk or be interested for anything.
What are your suggestions am I thinking too much?
I feel it won't be a good gesture to ask her directly if she isn't interested or anything.
Is she not interested? Something is definitely fishy. What do you suggest?
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