Dutch financial group ING has up to five bids for some or all of its for-sale private bank assets, a source familiar with the process said on Thursday, with offers for the full package running close to $2 billion.

Multiple sources involved in the deal identified Swiss firm Julius Baer and Singapore's DBS as two of the definite bidders.

The sale of ING's private banking assets is the most prominent transaction to date in the consolidation wave that is shaking up the wealth management industry after the subprime crisis.

The source familiar with the process said bids had been submitted for the Asian private banking unit, but were still coming in as of Thursday afternoon for the Swiss operations. There was also the possibility that some bids could come in after what had been a Thursday deadline, the source said.

It was not immediately clear who the additional bidders may be. A number of names have been rumored to be in or out of the process at various points over the last month, with only Julius Baer consistently seen as a front-runner.

ING declined to comment. Its shares, already up on the day, moved sharply higher as news of the bids broke.

The bidding, the source said, is split roughly evenly between those who want one piece of the package or another and those bidding for the whole thing. Bids for the full portfolio are closer to $2 billion than to the $1 billion that some analysts had speculated.

ING is selling the private banking businesses as part of a plan to raise 6 billion to 8 billion euros through asset sales, which it announced in April. That Back to Basics program follows a 10 billion euro state bailout the company received last October.

While ING has not recently broken out the assets under management for the units for sale, sources involved in the deal have said they stood around $35 billion at the end of last year and may have appreciated 20 percent to 30 percent since.

After the sale ING will retain its private banking operations in the Benelux region, which is its core market and where it plans to focus its efforts in coming years.

JULIUS BAER, DBS ON BOARD

Julius Baer, which is being advised by UBS, has bid for both assets, sources told Reuters. Both Julius Baer and UBS declined to comment. Switzerland's largest dedicated wealth manager has a strong capital base and has repeatedly said it is looking to grow through purchases.

Multiple sources with knowledge of the deal told Reuters that DBS Group, Southeast Asia's biggest bank, made a bid to buy the Asian private banking unit.

Lazard Ltd is advising Singapore's DBS, three sources told Reuters. It was not known immediately how much DBS has offered for these assets, but one of the sources said the bank would be conservative in its bid.

A DBS spokeswoman in Singapore declined to comment.

DBS, which is keen to expand in Asia, may be more attracted by ING's strong foothold in the Philippines and Indonesia, one of the sources said. But the bank, which is 28 percent owned by state investor Temasek Holdings TEM.UL, has also been handicapped by its reluctance to pay too much when bidding for assets.

While ING has been targeting a deal by the end of September, the source said the timeframe was not a firm deadline and that a final decision could slip beyond that.

ING shares rose 4.6 percent to 10.20 euros at 1248 GMT in Amsterdam. Through Wednesday the stock was up 47 percent from a recent bottom in mid-July. This week both J.P. Morgan and UBS raised their price targets on ING to more than 14 euros a share, a level the stock has not seen since early last October.

(Additional reporting by Kevin Lim in Singapore, Michael Flaherty in Hong Kong, Lisa Jucca in Zurich and Victoria Howley in London; Editing by Jon Loades-Carter)