The porn star's lawyer, Michael Avenatti, made the offer in a letter to Trump's lawyer, Michael Cohen, who has said he used his own funds to "facilitate" a payment of the same amount to Daniels days before the 2016 election.
Cohen has said that neither the Trump Organization nor the Trump campaign reimbursed him for the payment. The agreement itself was signed by Cohen and Daniels but not Trump.
In an apparent effort to link him directly to the deal, Daniels offered to "pay $130,000.00 to President Trump" by Friday. The letter says the offer will be withdrawn if it is not accepted by noon on Tuesday.
Neither Cohen nor lawyers who represent him responded to requests for comment Monday. The White House declined to comment.
The offer was first reported by the New York Times. A copy of the letter was provided to The Washington Post by Avenatti.
The existence of the agreement was first reported by The Wall Street Journal in January, and Daniels soon began speaking publicly, though not directly about her alleged affair with Trump.
Nearly two weeks ago, Cohen obtained a temporary restraining order against Daniels in private arbitration, where the contract says any disputes about the arrangement must be heard. Last week, White House press secretary Sarah Huckabee said "arbitration was won in the President's favor," language that suggested Trump was involved.
The letter also says she wants to be able to "use and publish" texts, photos and videos she may have from their relationship.
Daniels on Thursday gave a yet-to-be-aired interview to CBS News' "60 Minutes."
The offer of payment to Trump represents a shift by Avenatti, who said last week, "If she is ordered to return the money in order to invalidate the agreement, she will strongly consider doing so."
On Monday, Daniels joked on Twitter about how she would return the money: "I have toyed with delivering it gangsta style via private jet and cash in a gold suitcase. Alas I don't have a jet or gold suitcase. Suddenly I feel the urge to start rocking a giant diamond lightning bolt on a chain. (I'm kidding ... mostly)"
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