In a statement, Howard Wolfson said: "We now need to finish the job and ensure that Trump is defeated.
"But Mike is increasingly concerned that the current field of candidates is not well positioned to do that.
"Based on his record of accomplishment, leadership and his ability to bring people together to drive change, Mike would be able to take the fight to Trump and win," Mr Wolfson said.
But his advisers also acknowledge that Mr Bloomberg's belated entry to the race could present challenges in states like Iowa and New Hampshire, where other Democratic contenders have been campaigning for months.
The Bloomberg team are reportedly planning to focus on the so-called Super Tuesday contests in March, when 14 states, including California, Alabama and Colorado, will vote on a single day for their preferred White House nominee.
If he enters the race, Mr Bloomberg will face intense scrutiny of his three-term mayoral record in New York.
While in office, he defended the New York Police Department's use of the controversial stop-and-frisk policy, similar to stop-and-search in the UK, which critics say disproportionately targets African Americans and Hispanics. Black voters are a vital constituency for Democrats.
Speaking to reporters on Friday, President Trump said Mr Bloomberg "will fail" if he joins the Democratic race.
Candidates who want to get on the Democratic primary ballot in Alabama must submit the necessary paperwork by Friday.
New Hampshire's filing deadline is next week, on 15 November.
A New York billionaire as president?
So far this is only a single toe entering the water, but it's a significant one. The presence of the former New York mayor and multi-billionaire would set alight the race for the Democratic Party nomination.
The politician closest to Mr Bloomberg's centrist outlook is Joe Biden - but his campaign appears to be fading.
Mr Bloomberg has, I understand, been doing a lot of polling in early voting states like Iowa and New Hampshire.
This isn't the first time that he's eyed a run at the presidency, only to eventually decide against.
But in the past he's ruled himself out because he thought Americans wouldn't vote for a billionaire New York businessman. That concern no longer applies.
Who is Michael Bloomberg?
Mr Bloomberg's net worth is $52bn (£40bn), according to Forbes. This is nearly 17 times more than that of Mr Trump ($3.1bn).
Mr Bloomberg was a Wall Street banker who went on to found the financial publishing empire that bears his name.
A philanthropist, he has donated millions of dollars to educational, medical and other causes.
Originally a Democrat, he became a Republican to mount a successful campaign for mayor of New York City in 2001.
He went on to serve three terms as mayor until 2012, rejoining the Democratic Party only last year.
Regarded as a moderate Democrat, he has highlighted climate change as a key issue, but he had appeared to dismiss a potential run for the presidency earlier this year.
Mr Bloomberg is a large financial backer of gun-control advocacy group Everytown for Gun Safety, which he helped found in 2014.