Shares in Saab briefly ceased being traded on the Stockholm stock exchange on Thursday amid reports that the submarine deal was imminent.
Swedish daily Dagens Industri reported that Saab was likely to pay much less than the one billion kronor ($148.4m) previously speculated, with the deal instead expected to cost around 500 million kronor.
Saab issued a statement saying that talks were "ongoing".
In April Saab AB announced it had signed a non-binding memorandum of understanding regarding the purchase of the submarine maker Kockums from ThyssenKrupp.
"The discussions are at a final stage but still ongoing. An agreement with ThyssenKrupp Industrial Solutions AG has not been signed. Further information will be announced when negotiations have ended and an agreement is signed," the Saab group said in a statement.
Dagens Industri suggested the deal could be announced as early as Friday.
If the deal goes through it will bring to a close a turbulent few months of terse negotiations between the two companies.
Last October a source told The Local that Kockums was on the rocks due to "internal warfare" waged by its German parent company.
Saab then encountered the ire of ThyssenKrupp by poaching staff from Kockums before it attempted to swallow up the submarine manufacturer.
Tensions have been rising between the two companies after ThysenKrupp shut Kockums out from its major market in Singapore last Autumn.
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In April the Swedish military raided the Malmö premises of ThyssenKrupp, sparking further unrest between Saab and the German giant.
Kockums is understood to employ around 1,000 people at its Swedish hubs in Malmö, Karlskrona and the Muskö naval base.