The 18-year-old represented Arsenal and Rangers as a youngster before making the move to Derby, and he made his debut for the Rams in February of this year.
The attacker ended the 2021-22 campaign with one goal and two assists in 16 Championship appearances, but his contract is due to expire at the end of the month, and there has been a host of speculation surrounding his future over the last few weeks.
Man United were believed to be the favourites for the youngster, but according to Italian journalist Fabrizio Romano, Palace have won the race for his signature.
Romano claims that Ebiowei has already completed his medical with Palace and will sign a five-year contract with the Eagles despite interest from Old Trafford.
Derby will be entitled to a compensation fee for the youngster, although it will be significantly less than they could have sold him for this summer if he were on a long-term deal.
Meanwhile, according to Goal, Man United are preparing a move for Watford goalkeeper Daniel Bachmann, as they prepare for the departure of Dean Henderson to Nottingham Forest.
Henderson is expected to move on loan to Forest for the 2022-23 campaign, which would leave the Red Devils short of cover for number one stopper David de Gea.
Lee Grant has retired from professional football this summer, while Tom Heaton has also been linked with a move to the Championship.
Bachmann will allegedly be available for a fee in the region of £4m this summer following Watford's relegation back to the Championship for the 2022-23 season.
The 27-year-old made 12 Premier League appearances last term, while he has represented the Hornets on 41 occasions in all competitions since arriving from Stoke City in 2017.
Last month, Bachmann told Sky Sports Austria that Man United had made contact over a possible move to Old Trafford in the current market.
"There has been contact with Manchester United. It hasn't just fallen out of the sky... several clubs have shown interest in me - but the most intensive contacts have come from Manchester. It is a massive honour for a club like that to be interested in you," said the Austria international.
"I would be second choice behind David de Gea, who has been one of the Premier League's best keepers for years. But anything can happen in football. The performance principle applies. As a result, even big stars can sit on the subs' bench."
Newcastle United's Karl Darlow and Rangers' Robby McCrorie have also been linked with switches to Old Trafford as back-up to De Gea next term.