Groupon is testing out an offering of its own in the increasingly crowded payments space, according to an email I was forwarded by a business that was solicited for the service. (Disclosure: I have various puts against Groupon.)

The pricing is extremely aggressive, with a 1.8% transaction fee and a 15 cent per transaction charge for transactions processed through the terminal. Square charges 2.75% with no per transaction fee. PayPal Here and Verifone Sail charge 2.7%, also with no transaction fee. Groupon is charging 2.3% for AmEx transactions [update: a groupon insider tells me the AmEx pricing is 2.7, not 2.3]. Square and PayPal don’t charge extra, and Sail charges 3.7% for AmEx.

Unlike the other players, Groupon is offering an iPod Touch and card reader to merchants free of charge. (The others provide only the readers for free — that’s Square’s reader pictured above.)

The email hints at a forthcoming point-of-sale system for iPod and iPad and says the terminal is already in use in several places in the Bay Area.

Asked what he could tell me about the offering, Groupon spokesman Paul Taaffe replied, “Nothing.”

Groupon’s offering has the potential to put a lot of pressure on Square and could leave it with the least profitable customers. For customers whose typical transaction exceeds $15, it makes sense to use Groupon’s offering. On a $100 Visa transaction, Groupon would charge $1.95 vs. Square’s $2.75. That’s a 41% premium for Square.

Extremely low dollar transactions, such as the $4.34 I spend to buy an empanada at El Porteno, are money losers for Square because what it charges merchants doesn’t cover its transaction costs. (A crafty merchant looking to minimize fees could also put high dollar transactions on Groupon and run the $5 transactions on Square. That would be good for Groupon and bad for Square.)

Today’s announcement that PayPal will partner with terminal providers to target mid-market and large retailers could also limit Square’s ability to move up the food chain.

In March, Groupon acquired FeeFighters, a comparison shopping service for merchant accounts.

Although I have typically advised merchants to avoid most Groupon products, this pricing is compelling. The quality of the app is something I haven’t been able to assess yet.

It’s unclear what this means for Groupon as a company. It suggests that Groupon is trying a lot of different things. But payments processing is a highly competitive industry, and winning won’t be easy.