No. Absolutely not.
If your contract time was short, for example, only 3 months, and there is a company standard of at least a half year of probation, then it is ok if they want a further 3 months of probation time. But it is a rare case.
What I think the following possibilities:
I think that your employer wants to combine the advantages of the contract (they can always fire you, you are on continuous pressure a so work better) with the employment (-> lower wages). Employing somebody for a probation time, it would combine these advantages for him (and also the disadvantages, for you).
It is also possible, that there are company standards which you manager can't avoid (or he can only do with great difficulty). In this case, you can consider your probation time as a theoretical thing: you hadn't got the offer, if they wouldn't hire you.
How to decide between them, it can be decided only by you.
Asking something you can always do. At least it won't be accepted. I would suggest to not leave a company only because they didn't give your dream offer. But feel yourself entitled to look for a better one.
And also don't forget: being on probation time, it also means that you can always leave. For example, if you got a better offer.