Reports have suggested this week that the President-elect was courting the chief executive of the investment bank to fill the position, despite pledging during his campaign that he would cut government ties with major Wall Street banks.
According to Fortune magazine, Mr Dimon feels he is not suited to serving as the nation’s top ranking economic official.
JP Morgan spokespeople have declined to make any official comment about the idea of Mr Dimon joining the Trump administration.
Mr Dimon declined to comment through a representative.
Whatever the outcome, speculation about his departure from JP Morgan rattled some investors.
JP Morgan shares closed down 2.5 per cent on Wednesday night on speculation he might take the top job.
They have since edged up, trading up 0.38 per cent on Thursday afternoon.
"He is one of the best CEOs in the industry and corporate America, so if there were to be a quick departure that would be troubling," said Walter Todd, chief investment officer at Greenwood Capital Management, which owns JPMorgan shares.
"It is a very difficult decision to replace someone like him," he added.
On Twitter, Mr Trump has previously said Mr Dimon is a “good guy” and a “great banker”.
However he later critcised the chief executive for his decision to settle a $13bn fine with the US government calling it a "terrible move".
Although Dimon has said repeatedly and publicly that he would not want to be Treasury secretary, it is rare to reject a President-elect's request to join his Cabinet.
The move could put JP Morgan in an awkward position, because it would then be regulated by an administration Mr Dimon spurned.
Additional reporting by Reuters
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies