Taking an equity stake in Germany's only stock-market listed soccer club or a marketing alliance were options under consideration, the sources said.
"There have been talks recently," one of the sources said on Friday, adding the approach was at an early stage.
Both companies declined to comment.
Borussia Dortmund, from the Germany's rust belt Ruhr valley region, is seen as the only German club in a position to currently challenge the dominance of Bayern Munich.
Dortmund, Bundesliga champion in 2011 and 2012, finished second behind Bayern Munich in Germany's top league this season and also lost to Bayern in the cup final.
Dortmund may be taking a page from rival Bayern's playbook in seeking more corporate backing.
German insurer Allianz in February took an 8.33 percent stake in Bayern Munich for 110 million euros as part of a deal to help the club pay down debts on its stadium and to sponsor a youth academy.
The deal at the time gave the unlisted club, which is majority controlled by its members, an implied valuation of 1.32 billion euros (1.07 billion pound), more than five times Dortmund's market value of 250 million euros.
Sportswear maker Adidas and car maker Audi also hold minority stakes in Bayern Munich.
German magazine on Thursday reported that Deutsche Bank's co-CEO Juergen Fitschen had held talks over an alliance with Dortmund managing director Hans-Joachim Watzke.
Business daily Handelsblatt on Friday cited company sources as saying Deutsche might buy a 10 percent stake as part of a capital increase at the football club, which is due to enter Germany' small-cap index SDAX this month.
(Reporting by Kathrin Jones and Andreas Kroener; Writing by Ludwig Burger; Editing by Elaine Hardcastle)
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