By Christoph Steitz, Tom Käckenhoff and Arno Schuetze

FRANKFURT (Reuters) - Thyssenkrupp must swiftly cut ties to its ailing steel division in order to stop losses and rid itself of investments and liabilities it can't afford, two of its shareholders said a week ahead of the group's annual general meeting.

Thyssenkrupp is in discussions to sell its steel business to Britain's Liberty Steel, potentially putting one of Germany's most iconic businesses in foreign hands. Sources say it is also examining a spin-off of the business and wants to decide in March whether to divest or keep it.

Ingo Speich, head of sustainability and corporate governance at Deka Investment, the German conglomerate's 11th-largest shareholder, said: "The steel division is not sufficiently competitive and continues to be a shadow of its former self," adding big investments were needed to get it back into shape.

The unit may require up to 10 billion euros ($12.1 billion) in investments, although only 2-3 billion may be needed over the next couple of years, a person close to the matter said.

Liberty Steel, which is cash-positive, would benefit from annual synergies in a combination with Thyssenkrupp, a person familiar with the matter said, adding a 200-300 million euro estimate by Deutsche Bank was extremely conservative.

As part of its offer, Liberty Steel has pledged to secure jobs in a bid to win over sceptical workers, people familiar with the matter said.

"Such an offer sounds tempting, but requires a thorough examination by Thyssenkrupp," said Henrik Pontzen, head of sustainability of Union Investment's portfolio management.

"Billions of euros are still melting like butter in the sun. Thyssenkrupp must finally manage to stop the negative cash flow," he added.

Deka's Speich said that in case of a sale Thyssenkrupp needed to ensure to shake off the unit's liabilities, which amount to about 4 billion euros.

($1 = 0.8267 euros)

(Editing by Elaine Hardcastle)