The polls show some Americans are concerned about Mr. Biden's age because he will be 86 years old at the end of his second term if elected.
About 46% of respondents in the Reuters/Ipsos poll earlier this month said the phrase "Joe Biden is too old to work in government" accurately describes the president. 24% of Democratic Party members and 49% of independent Party members hold this view.
About 71% of respondents, including 52% of Democratic Party members, said they do not believe Mr. Biden should run for re-election in 2024.
Meanwhile, First Lady Jill Biden wants Americans to know that her husband, President Joe Biden, is planning to run for a second four-year term and she supports that - even though an official statement of his intention has not been made.
Responding to CNN, First Lady Jill Biden said she hopes Joe Biden will announce the campaign and dismissed the question of whether the80-year-old Democratic Party member may not run in 2024.
Of course I support that (re-election) - Ms. Jill Biden said.
The First Lady's opinion is considered important for the president's upcoming plans. She even made stronger comments to the AP news agency when asked if the president would run for re-election: "How many times does he have to say that for you to believe it?"
Democratic strategist Bud Jackson said that whether Mr. Biden should run for re-election in 2024 or not will continue to be a source of debate among Democratic Party members. Another election will see if voters are willing to give Mr. Biden, who is the oldest US president ever, another four years in office.
Mr. Biden himself has repeatedly said he intends to run for re-election and denied age doubts, but has yet to make an official statement.
"There are so many other things we have to complete in the coming time before I start the campaign," Biden told ABC reporter at the White House.
Last November, Mr. Biden said he would decide whether to re-elect in early 2023, but so far he has not made a statement.
So far, Mr. Biden has not faced any major opponents and he has not shown any rush to officially re-elect.
Earlier this year, Mr. Biden took the time to address the confidential documents discovered in his old office, and recently the focus on foreign policy - including a surprise trip to Ukraine - has dominated the president's schedule.
Cedric Richmond, a former White House adviser to Mr. Biden, said the president would announce " whenever he was ready" when asked whether a re-election announcement would be made in March or April.
Re-election efforts may be strongly affected by Mr. Biden's White House advisory team. The campaign manager and the location of the president's campaign headquarters have not yet been determined.
On the Republican side, former President Donald Trump - who will be 78 years old at the time of the 2024 election - and Ms. Nikki Haley - former US Ambassador to the United Nations, former Governor of South Carolina - have so far declared themselves a candidate for 2024.