It sounds as if you have the drive formatted as FAT and Time Machine must be backed up to a drive formatted as HFS+
You have two options.
Buy a new drive for the back up.
Use third party software to re partition the existing drive - like gparted Click Here. You must be very careful using such tools that you do not do something wrong with the result you loose your data.
Data should always be on at least two independent storage mediums. If that is not currently the case then getting a new hard drive may be the best solution.