The testimony of the many stories that involve Outsiders and the logical structure of their existence suggests that they would be interested in

If you read enough of the many known space stories you'll actually find quite a bit of evidence:

* They lease space on Triton (first see in *At the Core*, and it comes up several times after that)
* The sell Elephant the coordinates of "The most unusual planet in known space"
* They deal with the puppeteers and the colonists repeatedly in the *Fleet of Worlds* series and it's prehistory (the primordial deal for the planet drive is also discussed in *Ringworld*).
* The sell the humans of We Made It the hyperdrive early in the first Man-Kzin war

What we take from that is that the Outsiders do a lot of business for as little contact as they have with warm species. They seem to accept payment in

1. Information (as [suggested by zephyr][1]) or technology (though in the *[Fleet|Juggler|Destroyer|Betrayer of Worlds][2]* books it is made clear that the races of Known Space have little to offer in this respect with an exception related to reason (3)). Because those are things that they can take with them, and re-sell again and again.

2. Credit expressed in a local currency that they can expect to use (as [geoffc notes][3]), which means offered by races that are politically stable and sufficiently well established to have a expectation of lasting a long time.

  That said their willingness to sell the hyperdrive to We Made It suggests that they are willing to take a chance on up-and-coming races.
3. Spoiler reason (read the *Fleet of Worlds* series first)

  >! Protection of their juvenile stage: the star seeds.


  [1]: http://
  [2]: http://www.sfwa.org/members/lerner/fleetseries.html
  [3]: http://scifi.stackexchange.com/a/4456/231