Travelocity’s parent company, Sabre, has been busily selling off assets, presumably in anticipation of a 2014 IPO try, and its household name online travel agency likely is the next piece of the empire on the block.

But does anyone want to buy Travelocity?

Considered the fourth or fifth largest U.S.-based online travel agency as it jockeys with CheapOair for the fourth position, Travelocity has a recognized brand, owns LastMinute.com in Europe, has a weak hotel business, and the last time its numbers were leaked, Travelocity’s revenue was taking a substantial hit.

Part of privately held Sabre, Travelocity’s revenue declined 6.6% annually in the 2009-2011 period, largely due to market share gains from other online travel agencies, and hotel and airline websites, as well as relatively weak terms in its airline agreements. Travelocity’s revenue fell 5.3% in 2011 to $825.3 million.

As one competitor put it, “Travelocity is a drag on a hugely successful business.”

Apart from Travelocity, which was king of the online travel agency hill more than a decade ago, but has struggled for an extended period, Sabre’s global distribution, airline and hotel IT businesses are seemingly healthy, and could paint a semi-healthy picture for investors contemplating dabbling in the hoped-for IPO.

An IPO wouldn’t be a slam dunk, though, as GDS competitor Travelport found out in 2010 when it abandoned an IPO try.

Sam Gilliland, the CEO of Sabre, which is owned by private equity firms Texas Pacific Group and Silver Lake Partners, has stated publicly — duh — that an IPO would eventually be on Sabre’s agenda.

Sabre has been cleaning things up in anticipation of a public offering, selling its Singapore-based online travel agency Zuji to Webjet in 2012, and off-loading Holiday Autos to CarTrawler and Travelocity Business to BCD Travel last month.

Travelocity has failed to build a global hotel business that can even get into the conversation with Priceline/Booking.com and Expedia, got distracted for years with its 2005 acquisition of LastMinute.com, and doesn’t have a suddenly sexy travel-metasearch business (with apologies to its smallish iGoUgo unit) along the lines of Priceline’s Kayak or Expedia’s Trivago.

The party line is that Sabre considers Travelocity a core asset, but we have come to learn that the Sabre board is split on whether to dispose of Travelocity or not.

Keeping Travelocity would certainly complicate a potential Sabre IPO roadshow next year if Travelocity hasn’t managed a turnaround, and the question of a sale would of course depend on what sort of offers roll in.

Acquiring Travelocity wouldn’t do much for Expedia, Priceline or Orbitz, and long-time Travelocity partner Yahoo likely wouldn’t be interested in acquiring a flight-heavy, travel-transaction business.

A sale of Travelocity and its Roaming Gnome lawn ornament and mascot could spark some interest from an Asia-Pacific or European online travel agency looking to hasten an entry into the U.S.

Australia-based Webjet could be a candidate, althought it acquired Travelocity’s Zuji unit last year, and presumably could have worked out a package deal including Travelocity if Webjet was truly interested.

Australia-based Flight Centre, which owns U.S.-based Liberty Travel and FCm Travel Solutions, a corporate travel agency, could be tempted to take a closer look at Travelocity to embolden Flight Centre’s U.S. profile.

And, some speculate that private equity-funded Odigeo, which has been collecting online travel agencies in Europe, including Opodo and eDreams, may want to consider adding Travelocity and LastMinute.com to the family.

A sale of Travelocity isn’t a sure bet, but it certainly would be welcomed by Sabre in its attempted return to the public markets.

A spokeswoman for Sabre declined to comment on “rumors or speculation.”

Photo Credit: The Roaming Gnome, Travelocity's brand advocate, could be wandering anew if Sabre finds a buyer for Travelocity. Travelocity