The BBC reports he would have been entitled to a bonus of up to £2.75m, based on 250% of his £1.1m salary.
In a statement, Jenkins said taking the bonus “would not be right, in the circumstances”. It is the second year in a row he has refused to take his bonus entitlement.
In a statement released yesterday, he said: “2013 has been a year of considerable positive change for Barclays, and I am particularly proud of the progress we have made in starting to rebuild trust, in defining and implementing a common culture, in repositioning the business for the future, and in significantly improving our balance sheet.
“While all of these actions are in the long-term interests of our shareholders, I am aware of the very significant costs which have been required to address legacy litigation and conduct issues in 2013, as well as to exit assets and businesses we no longer wish to participate in.
“When combined with the substantial rights issue we completed in the autumn, I have concluded that it would not be right, in the circumstances, for me to accept a bonus for 2013, and I have therefore respectfully declined the one offered to me by the Board.”
He took over at the bank in August 2012.
