* Merger partner Popolare di Vicenza lost 1.9 bln euros in 2016
* European Commission sees possible solution on bailout request
* Sources say accord over state aid within reach (Adds details, comment by European Commission)
By Valentina Za and Francesco Guarascio
MILAN/BRUSSELS, April 3 (Reuters) - Italian lender Veneto Banca reported a heavy loss on Monday and a drop in customer deposits, highlighting its precarious position as it seeks EU approval for a state bailout it requested alongside fellow bank Popolare di Vicenza.
After a meeting with the Italian authorities on Monday, the European Commission expressed confidence a solution for the two northeastern regional banks could be found in the coming weeks.
"All players are sitting around a table with the objective of coming to a common solution that is efficient, sustainable and in the interest of financial stability," a Commission spokesman said.
Italy is keen to avoid a restructuring of the two Veneto-based lenders under strict new EU resolution rules that inflict losses on bank creditors and large depositors, as it fears it would damage confidence further in its ailing banking system.
Rome wants to inject public money into Italy's fourth-largest bank Monte dei Paschi di Siena as well as the two banks, using an exception to the rules that would limit the number of creditors taking a hit.
European regulators have judged Monte dei Paschi to be solvent, a necessary condition for a state bailout, but Popolare di Vicenza and Veneto Banca have not been deemed viable yet.
A Treasury source said on Monday there was a confidence that any hurdles could be overcome soon. Another two Italian sources familiar with the matter said a solution appeared in sight.
Veneto Banca posted a 1.5 billion euro loss for 2016 mostly due to writedowns of doubtful loans totalling 1.3 billion euros. It also booked 434 million euros in provisions and charges related to disputes with shareholders who saw their investments wiped out when the bank had to be rescued last year.
A week ago, Popolare di Vicenza reported a 1.9 billion euro loss for 2016, prompting investors to dump its senior debt on worries it may not qualify for a state bailout.
Both banks have a core capital that is below the minimum thresholds set by the European Central Bank and have been losing deposits.
Veneto Banca said that given how quickly its liquidity could worsen it would tap a state guarantee to issue up to another 1.4 billion euros of debt, which would come on top of a similar 3.5 billion-euro issue in February.
The two banks were rescued from bankruptcy only a year ago by Italy's state-sponsored, privately-funded banking industry rescue fund Atlante, which has pumped 3.4 billion euros in capital into them - broadly equivalent to their combined 2016 loss.
Together they had already lost nearly 5 billion euros in 2014-2015 and are estimated to need as much again in fresh capital.
Atlante, funded by Italy's top banks and insurers, has pinned its turnaround hopes on a merger of Popolare di Vicenza and Veneto Banca. Both banks have said their merging is essential but have warned it is still uncertain as to whether approval will be granted by the ECB. ($1 = 0.9379 euros) (Additional reporting by Stefano Bernabei; Editing by Greg Mahlich)