Japan's Sumitomo Mitsui Banking Corp. is nearing a deal to buy General Electric Co.'s European private-equity finance business, according to people familiar with the matter, the latest step in the industrial conglomerate's retreat from banking.

SMBC is expected to pay more than $2 billion for the unit, known as a sponsors unit and which finances buyouts and other transactions for private-equity firms in Europe, said the people. They added that a deal could be announced as soon as Tuesday.

The Japanese bank prevailed over other bidders including Apollo Global Management LLC and Ares Management LP, they said.

A spokesman at SMBC said nothing specific has been decided at this moment.

A deal comes on the heels of GE's agreement to sell its vehicle-fleet financing businesses in the U.S., Mexico, Australia and New Zealand for $6.9 billion, and a separate deal for its European fleet business, both announced Monday.

GE is shedding a large portion of its GE Capital business's $500 billion in assets. Earlier this month, it agreed to sell its U.S. private-equity lending unit to Canada's largest pension plan in a deal valued at $12 billion.

The sponsors deal doesn't include GE Capital's stake in its three billion-euro ($3.4 billion) joint venture with Ares, which also lends on private-equity deals, one of the people said.

SMBC has been keen on buying some of GE's assets, including its Japanese finance unit and U.S. railcar leasing business, people familiar with the matter have said.

SMBC also is no stranger to the European leveraged finance business, entering the market in 1997, according to its website. The bank's European unit has around $1.9 billion of outstanding commitments, having provided loans to buyout and other transactions, its website says.

GE's withdrawal from banking follows investors urging the company to return to its industrial roots as market conditions and federal regulations weighed on returns.

Atsuko Fukase contributed to this article.

Write to Gillian Tan at gillian.tan@wsj.com and Ted Mann at ted.mann@wsj.com

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