Fox anchor Maria Bartiromo tonight tweeted she had heard Dimon was about to be offered the role, with a “big meeting” expected tomorrow.
However, the JP Morgan boss has previously publicly stated he would not be interested in the role.
Bartiromo later backtracked, stating it was now between former Goldman Sachs partner Steve Mnuchin and Dimon, and the final name would not be known until the end of the week.
Dimon has said publicly "not suited for job/staying @jpmorgan" but its down to him and Mnuchin. We won't know for sure until end of week— Maria Bartiromo (@MariaBartiromo) November 16, 2016
Also tonight, reports emerged suggesting the US bank was close to settling over claims it had hired relatives of key Chinese decision makers to win business.
JP Morgan declined to comment on either issue.