It has already produced lots of seeds. And it will continue to do so until it dies. To collect the seeds, make a little bag with the toe end of some pantyhose and tie it firmly (but not too tightly) around one of the flower stalks. Seeds should fall into the bag once they're ripe. They aren't the easiest of seeds to collect!

Thanks, that is a great idea to capture the seeds, I'll have to try it.

Do you think I should re-pot the basil or just plant a new one?

My plain basil plant is now 2 yrs old. But I pinch off the flowers early and protect it from the cold. I'm in Tampabay which is zone 9b

I would keep the one you have but also plant those seeds for more plants. I would never waste a plant if it is useful.
Here in Texas I have grown basil and have not even bothered to harvest the seeds until the next spring. The seed pods do not seem to open they will stay on the plant thru out the year if you forget to harvest them. We do have a nursery that does go down into Mexico and other areas to harvest seeds over the years, they use the paper bag capture system and they are now known throughout the world for saving seeds of many different plants which they sell.

Thanks for the info. The way the basil was growing I thought it was going to die soon after it seeded but it seems to keep growing.

@bellashere - I live in Qld, Australia, it barely gets below 20C (68F) here during winter so I don't need to worry about protecting them from the cold.

@wally-1936 - I will keep it, it seems to continue to seed so why not. I heard of using a plastic bag to put the stalks in and shake it but it might work better with a paper bag.

Thanks

The way I get basil seeds is wait until the flower stalks turn brown and put my fingers down low on the stem. Strip the dried flowers off by pulling up and letting the stem slide thru my fingers. That way I have a handful of dried flowers containing seeds. Put them all in a strainer with holes big enough for the seeds to fall thru. Dry on a paper plate a few days and put in an envelope or re-plant. Basil seeds make good tasty sprouts and can be eaten in salad/sandwich at any stage.