Try contacting Pier 1 and see if they can either make bigger pillows for you or find the fabric for you.

Thank you. They said that they don't make them in larger sizes and can't help me with the fabric.

Aargh. A few phone calls is all it would take them.

It's against policy of many retailers to provide the name of the manufacturer for furniture or fabrics used in items that they carry.

Yep. $$ more important than helping people.

I'm sure they could have given me more information if they wanted to, but I wasn't surprised. Oh well.

Not exactly the same, but there are many similar tapestry wovens out there -- click image for link to fabric:

Here is a link that might be useful: Contemporary woven browns

Whoops! I read your post too quickly as "larger circles than this". Well, you might be able to track down similar fabrics in the link I added. Happy hunting!

You can check the pillows to see if they are seamed on all 4 sides; if not, you might be able to open them and resize, either by combining two pillows, or applying the fabric to a solid color pillow, maybe framing the circled fabric, or just solid on the back.
Kind of like this:

you could trim others to coordinate:

This fabric looks similar to the fabric on chairs in the condo we're living in temporarily. Broyhill is the manufacturer, and I think the chair style is Hollis. You could check the upholstery selection at furniture stores in your area that sell Broyhill, or you could possibly search options online.

circuspeanut, thanks for trying to help. I did go to the link to look for the same fabric and couldn't find it. I also looked everywhere I could think of, but no luck.

olychick, this pillow has a solid white backing with a zipper. Therefore, I may be able to combine a couple of pillows to make them larger. I also like the look of the pillows you found that are different but tie in together. Cool idea.

jujubean, that fabric on the chair is very much like mine from the looks on my monitor. I went to Broyhill's website and other websites that sell Broyhill in hopes of finding the fabric identical to mine. No luck, but it's got to be out there somewhere, I would think.

I may have to go with something else. At any rate, I appreciate all your help.