The Gateway offices are occupied by Citi, the global financial services group.
Selling agents CBRE say it is the largest office investment to come onto the market in Northern Ireland in the last decade.
In 2014, Ulster Bank sold most of its Titanic Quarter loans to the US hedge fund Davidson Kempner.
Such a fund will typically look to get a return on its money within a few years either through asset sales or loan refinancing.
The Gateway offices are likely to be attractive to institutional investors such as pension funds.

The deal will see the 24-year-old loose-head remain at Kingspan Stadium until 2019.
"This season has been particularly pleasing because I have played a lot more than I expected to," said McCall.
"I'm grateful to Les Kiss for giving me an opportunity to prove myself this year," added the front-rower.
McCall's outstanding form this season was recognised at the Ulster Rugby Awards Dinner earlier this month when he collected the Young Player of the Year award.
He made his Ulster debut against Leinster in March 2013 and made three further appearances before earning his first start, against Dragons in November last year.
He went on to start five of Ulster's six Champions Cup games, scoring his first senior try in the dramatic 24-23 away win over Oyonnax in January.
"I want to continue to work hard to develop my core skills and try to push my game on to the next level," explained McCall.
"Hopefully I can cement a starting position next season and contribute to a successful Ulster team in the Pro12 and Europe."
Ulster Director of Rugby Les Kiss described the news as "another great boost for us, following on from the news that Stuart McCloskey has also signed a contract extension".
"Kyle's incessant work-rate has seen him earn a reputation as one of the best trainers in the squad. At 24, he is still young for a front row player, and with his huge potential and desire to be the best that he can be, I've no doubt that he can become a future international."
An office development in Belfast's Titanic Quarter has been put up for sale with a price tag of £29m.
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Prop Kyle McCall has become the latest Ulster player to commit his future to the province after signing a two-year extension to his current contract.