* Several options for divestment still on table - source
* Brazilian paper says CSN has been picked as buyer
* ThyssenKrupp shares up 3.7 percent (Recasts, adds source, background shares)
FRANKFURT, July 16 (Reuters) - The planned sale of ThyssenKrupp's Brazilian steel mill is unlikely to happen quickly, a source close to the transaction said after a newspaper reported that a deal had been struck.
"The process has gained momentum of late, but it would be a miracle if a decision could be reached within the next couple of days," the source said on condition of anonymity because the talks are confidential.
The German steelmaker has been trying to offload its loss-making Steel Americas business, which comprises the Brazilian CSA mill, and a plant in Alabama in the United States as it shifts investment to higher-margin products and services such as elevators, submarines and parts for manufacturing plants.
"There are still several options on the table and we are not at a stage where we would say we were pressing ahead with one of the options," the source said.
Brazilian newspaper O Estado de Sao Paulo had said in an article published on its website late on Monday that ThyssenKrupp had agreed to sell a majority stake in CSA to Companhia Siderurgica Nacional (CSN), giving no details of its sources.
Under the agreement, CSN would control about two thirds of CSA, with ThyssenKrupp retaining a small stake, the paper said.
It said the deal would be announced in the coming days, once it has been approved by Brazilian miner Vale, which owns 27 percent of CSA.
ThyssenKrupp declined to comment on details of the negotiations and reiterated that it aimed to agree a deal shortly. CSN was not immediately available for comment.
ThyssenKrupp has struggled to find a buyer willing to pay its price for all or part of Steel Americas. The German company has had to write down the value of the business to 3.4 billion euros ($4.4 billion) over the past year, from more than 7 billion euros.
Steel Americas cost 12 billion euros to build but lost 1 billion euros in the 12 months to Sept.30 last year.
One of the options being discussed for the Brazilian part of Steel Americas is a joint venture through which ThyssenKrupp, CSN and Vale would each hold a third of CSA, sources familiar with the deal have said.
Sources have said that negotiations have centred around the valuation of the business and the question of who will have to make necessary investments in Brazil of $700-800 million.
ThyssenKrupp shares rose 3.7 percent to 15.92 euros by 0925 GMT, making it the biggest gainer on Germany's blue-chip DAX index, which was down 0.2 percent. ($1 = 0.7664 euros) (Reporting by Arno Schuetze; Additional reporting by Maria Sheahan and Filipa Cunha-Lima; Editing by David Goodman)