The OP says the value (I meant price) of the underlying asset. I.e. S, not F. Thus, given the price of the call option, and S, K and T, how do we get a closed form value for r, the implied interest rate? I don't think there is a solution, although we can use numerical methods.
Clearly if we are told what the forward is, or the put price, or that it is ATM, then we can solve closed form. Otherwise not. Perhaps I am wrong.