(CNN) -- Plans are in motion for President Joe Biden to formally announce his bid for a second term as soon as next week, with a campaign-style video set to be released to definitively answer the question of whether he will run again and igniting an aggressive fundraising effort to help Democrats hold the White House.

Biden's small circle of close-knit advisers and allies are preparing for a video announcement Tuesday that would coincide with the anniversary of Biden's 2019 campaign announcement, according to four sources familiar with the matter.

Advisers inside and outside the White House caution that timing could still change, pending unforeseen events, but a decision has been reached that it is "no longer helpful or necessary to not just say the obvious: He's running," a senior Democratic official told CNN.

Both sentimental and fond of an anniversary, Biden has signed off on a plan to formalize his intentions as soon as Tuesday, four years after he stepped back into public service to launch his campaign in 2019.

The importance of the connection to the anniversary and the fact that it would come just days before the first major donor gathering next Friday have made the possibility increasingly likely, one of the people said.

Biden's plan to run for reelection has been an open, if not officially announced, reality inside the West Wing for months.

His official declaration, which will end any lingering speculation about his intentions, sets off a battle to convince the public of his accomplishments and his ability to continue serving well into his eighties.

Biden said last week he had completed his "calculus" about mounting a reelection bid and would announce his intentions shortly.

"I've already made that calculus. We'll announce it relatively soon," Biden said as he departed Ireland. He'd just concluded a campaign-style rally, one of the largest of his career.

"The trip here just reinforced my sense of optimism about what can be done," the president told reporters.

"I told you my plan is to run again," he said.

Biden's aides have been quietly putting an infrastructure in place for a reelection campaign for months. The effort has been led at the White House by deputy chief of staff Jen O'Malley Dillon and senior adviser Anita Dunn.

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