Customer says that he is already working with a vendor in the same space. How do I stay in the mind of this potential customer and remain an option?

there are a lot of ways but the most important thing is to create value and make a loyalty program to save your position and invest in your brand   

A book on sales technique would cover this in the chapter called "overcoming objections".  There are lots of things you can do but they boil down to two objectives - learning as much as you can about the competitor, and developing the relationship with the client.  It's good if you can show examples of other companies in his industry who have recently changed to you, and unshakeable confidence in your own product also helps.  Don't go straight for a hard sell - you'll just push him away.  If all else fails get the customer's permission to contact him in a few months: point out that it's his job to keep on touch with the market anyway. 

Follow-up with the customer is good option

Try influencing the customer the benefits of your company over rival vendor.