Deutsche Bank is seeking to replace Chief Executive John Cryan amid an intensified boardroom row over the bank's future and alarm at its performance, the Times newspaper reported on Monday.
Deutsche Bank was not immediately available to comment on the London newspaper's report.
Gnodde, who is a vice chairman of Goldman Sachs, is said to have been pursued by the lender amid a breakdown between Cryan and Deutsche Chairman Paul Achleitner, the Times said.
Goldman Sachs did not immediately respond to a comment.
Gnodde is believed to have turned down the proposal. Other possible replacements considered are Jean Pierre Mustier, chief executive of UniCredit SpA, and Bill Winter, chief executive of Standard Chartered, according to the Times.
Cryan and Achleitner are said to have disagreed over their approach to HNA Group, the Chinese conglomerate which became the German bank's largest shareholder, the Times reported.
Cryan and Deutsche Bank's chief financial officer, James von Moltke, were involved in a bitter board dispute over the bank's future, arguing for a more radical restructuring that included a complete overhaul of its investment banking division, the Times said, citing a source.
"It is quite clear the relationship is broken between the chief executive and the chairman", the Times quoted the source as saying.
Earlier this month, Deutsche Bank warned on costs for 2018, citing delays in some business disposals, even as the lender said it expects revenues to rise for the full year.
It also said its bonus pool would be above 2 billion euros ($2.49 billion) as the loss-making bank seeks to retain staff during a major overhaul.