The 48-year-old has been without a club since ending his five-year spell on Tyneside in July, but his name has remained prominent in discussions about potential managerial appointments across the Premier League.
According to The Sun, Palace approached Howe about replacing Pierre Sage, who was dismissed on Monday following a disappointing start to the season.
Sage lasted just 10 Premier League matches after succeeding Oliver Glasner, with Palace sitting bottom of the table on seven points. Four consecutive league defeats ultimately proved decisive, including Sunday's 3-1 loss against Liverpool at Selhurst Park.
However, Howe was not prepared to take the opportunity at Selhurst Park, leaving Palace to concentrate on alternative candidates.
Former Tottenham Hotspur and Brentford manager Thomas Frank is reportedly the leading contender, while Sean Dyche is also under consideration.
Frank has been out of work since leaving Tottenham in February, while Dyche offers considerable experience in dealing with clubs fighting against relegation. Both would bring different qualities to a Palace side urgently needing to reverse its fortunes.
Howe's decision is particularly interesting given previous indications that he is ready to return to the dugout. After leaving Newcastle United, the Englishman explained that he wanted time away from football to recharge before deciding on his next challenge.
His achievements at Newcastle have ensured that he remains an attractive proposition for clubs seeking an experienced Premier League manager.
Howe helped transform the Magpies into Champions League contenders and delivered the Carabao Cup in 2025, ending the club's long wait for a major domestic trophy.
Before his time on Tyneside, he established his reputation at Bournemouth, guiding the club from League Two to the Premier League.
His name has also been linked with Manchester United, where Michael Carrick's position has come under scrutiny following a difficult run of results.
Reports have suggested that Howe has been studying United's situation and considering the possibility of taking charge should the club decide to make a managerial change.
He is understood to be among the leading candidates if the Old Trafford hierarchy decides Carrick's tenure should end.
There is also an indication that United's ownership would prefer an English manager, making Howe an attractive option given his Premier League experience and previous achievements.
For Palace, however, his rejection means the search for Sage's successor must continue elsewhere.
The London club need an appointment capable of restoring confidence quickly, particularly with the threat of relegation becoming an increasingly serious concern.
Howe's decision suggests that, although he is prepared to return to management, he is being selective about the next project he takes on.