Can the vale of call option be negative?

No. The value of a call option can never be negative. For example, let's say that one has a call option on FOO with a strike price of $30 and the option expires at the end of the day.

If the underlying price of FOO shares are below $30, the price of the option will be very near $0 (because no one would pay much for the right to pay for an underwater option), but there is still a chance that the stock will go above $30 (no matter how remote).

If the underlying price of FOO shares are at $30, the price of the option will be low, but positive (because there is a chance that the stock will go above $30.

If the underlying price of FOO shares are above $30, the price of the option will be slightly higher than the difference between the strike price and the share price (because there is so little time left for changes; however, there will be some time value as suggested in the examples above).