By Silvia Ognibene

FLORENCE, Italy (Reuters) - The chief executive of Monte dei Paschi di Siena <BMPS.MI>, Fabrizio Viola, and the Italian bank's former chairman, Alessandro Profumo, are under investigation for alleged false accounting and market manipulation, a source with knowledge of the matter said.

The investigation, which started in 2015 following complaints filed by small shareholders and consumer associations, comes as the Tuscan bank prepares to launch a 5 billion euro ($6 billion) stock sale after emerging as the weakest bank in Europe in industry stress tests in July.

A spokesman for Monte dei Paschi said the decision to investigate Viola and Profumo followed a proposal by two shareholders to seek damages from the two executives which was rejected by other shareholders at an April meeting.

"(Under Italian law) prosecutors are bound to open an investigation when they receive a complaint," the spokesman said in an emailed comment.

This comment reflects Profumo's position, a separate spokesman for Profumo said.

Being placed under investigation in Italy does not imply guilt and does not automatically lead to charges being laid.

The source said on Thursday prosecutors in Siena alleged the bank did not correctly book two derivatives trades known as Alexandria and Santorini between 2011 and 2014.

The inquiry was transferred to prosecutors in Milan in July. They now have 18 months to decide whether to shelve the investigation or seek trial for Viola and Profumo, the source said.

Siena prosecutors could have chosen to close the case, the source added.

Reuters' calls to the prosecutors' offices in Milan and Siena went unanswered.

The health of Italy's third-largest lender poses a threat to the wider banking system, the savings of thousands of small investors and also to the weakening political standing of Prime Minister Matteo Renzi, who faces a make-or-break constitutional referendum in the autumn.

Viola and Profumo were drafted in at Monte dei Paschi in 2012 to turn it around after it wrecked its balance sheet by overpaying on the purchase of rival Antonveneta in 2007 and engineering risky derivatives trades.

Profumo, a veteran Italian banker formerly at UniCredit <CRDI.MI>, stepped down as Monte dei Paschi chairman in August last year after overseeing two cash calls in 2014 and 2015 which raised a total of 8 billion euros.

Shares in Monte dei Paschi are trading at record lows, after losing around 86 percent of their value since the bank completed its last share sale in June 2015.

In January, Milan prosecutors sent to trial 13 former managers at Monte dei Paschi, Nomura <8604.T> and Deutsche Bank <DBKGn.DE> in a separate investigation into the two derivatives as well as a hybrid financial instrument used to partly finance the 2007 acquisition.

All the managers involved and the banks have denied any wrongdoing.

Prosecutors have said the bank's former management entered Alexandria and other derivative trades to conceal losses after stretching its finances to buy Antonveneta for 9 billion euros.

The Monte dei Paschi spokesman said on Thursday the Milan prosecutors had acknowledged the bank's new management was actively helping to shed light on those responsible for the trades.

In December, Italy's market watchdog Consob told Monte dei Paschi it had inaccurately booked the Alexandria derivative trade in its 2014 and first-half 2015 accounts.

($1 = 0.8834 euros)

(writing by Valentina Za and Stephen Jewkes, editing by Anna Willard)