PARIS, June 10 (Reuters) - Societe Generale is struggling to agree a deal for its securities services unit, with potential bidders balking at the price the French bank wants for the business, sources close to the matter said.

France's third-biggest listed lender has been trying to offload Societe Generale Securities Services (SGSS) since last year, the sources said, as part of wider efforts by Chief Executive Slawomir Krupa to dispose of assets and streamline the bank.

The bank is seeking more than 1 billion euros ($1.1 billion) for the unit, according to media reports.

U.S. bank State Street, one of the world's largest asset custodians after market leader BNY Mellon, has been in talks to buy SGSS but the discussions have stalled, one source said.

Both SocGen and State Street declined to comment.

While SocGen remains open to a sale at the right price, the bank has decided selling SGSS is no longer a priority given the unit provides a regular stream of liquidity that other parts of the business need, two of the sources said.

The sources declined to be named because of the sensitivity of the matter.

Other potential buyers include CACEIS, the asset servicing business France's Credit Agricole co-owns with Spain's Santander. CACEIS recently bought RBC Investor Services' European activities.

SSGS provides the likes of asset managers and pensions funds with services such as custody of assets.

The business saw its revenues fall 17.5% in 2023, SocGen said in its annual report. The unit delivered 849 million euros in revenues in 2022.

SGSS had 4.9 trillion euros in assets under custody at end-December, making it the second-biggest assets custodian in France after BNP Paribas.

SocGen in April agreed to sell its professional equipment financing business to French rival BPCE for 1.1 billion euros. The bank also agreed a sale of its Moroccan units in April, and in December SocGen announced a deal to sell two African subsidiaries in Burkina Faso and Mozambique.

At market open on Monday, SocGen's shares had risen by close to 12% since a poorly-received strategic plan presented by Krupa last September. By comparison, the STOXX Europe 600 banks index rose by close to 34% over the period.

SocGen's shares fell by around 7.5% on Monday after French President Emmanuel Macron called a snap parliamentary election, spooking markets.

($1 = 0.9234 euros) (Reporting by Mathieu Rosemain Editing by Tommy Reggiori Wilkes and Christina Fincher)