Options granted by an employer to an employee are generally different that the standardized options that are traded on public stock option exchanges. They may or may not have somewhat comparable terms, but generally the terms are fairly different.
As a holder of an expiring employee option, you can only choose to exercise it by paying the specified price and receiving the shares, or not. It is common that the exercise system will allow you to exercise all the shares and simultaneously sell enough of the acquired shares to cover the option cost of all the shares, thus leaving you owning some of the stock without having to spend any cash. You will owe taxes on the gain on exercise, regardless of what you do with the stock.
If you want to buy publicly-traded options, you should consider that completely separately from your employer options other than thinking about how much exposure you have to your company situation. It is very common for employees to be imprudently overexposed to their company's stock (through direct ownership or options).