This is a great alternative for those in your situation. It's a faux-bois long plank tile. The better tiles have a texture like wood grain, not just a printed image, it feels good under foot and is very beautiful.

The Italian product shown here is no longer in production, but any tile showroom- not home imporvement store- will be able to source many versions of this. Comes in all different colors.

You don't have to glue it down. You can do a "floating floor" installation, where the installer will leave fractions of an inch at the edges of the room (for temperature shifts) which will be covered by the baseboard. However, I am not sure if radiant heat will be ok for the engineered wood planks. Shannon's recommendation above of porcelain tiles that look like wood planks might be a better choice. They make them so realistic today you cannot tell the difference.

A floating floor is one of your best options. Engineered hardwood (so long as you purchased the "floating" type) does well in basements so long as you take the necessary precautions of a vapour barrier (yes, this still has to be done) over the slab and then the engineered over top.

Please ensure that the manufacturer ALLOWS for installation over in-floor radiant heat (some producers do NOT allow) before doing any form of installation. Please be aware that there are some very specific concerns with wood and radiant heating. The heating system can only be adjusted by 5 degrees in 24 hours. Wild swings in temperature are not "allowed" when wood is installed over radiant heat (I know because our cork floating floors have all the same issues - they are a form of wood and wood needs to adjust slowly).

Humidity must be maintained between 45%-65% throughout the year for most woods. With a floating floor you should be looking at some form of underlay as well or else the planks are going to "slap" against the cement - and the echo is going to be rather annoying. The underlay must be approved for infloor radiant heat.

Floating over radiant heat is the way to go with engineered products.

Agree with Cancork that an Engineered floor must be rated for radiant heat. This mostly has something to do with suitable wood species. Each manufacturer will have its own guidelines, but in our experience hickory wood is usually a tough one to put over radiant. There are others as well.

Also, we would recommend click or drop lock hardwood over tongue and groove gluing. See photo for example.

Nice response by Cancork Floor Inc. Their right, installing underlayment is important to avoid additional acoustic issues, also it just has a more solid feel beyond accommodating moisture control. We have used a product called Regupol successfully.
Hope that helps.