The 24-year-old made a big-money move to the Nou Camp after six years at Valencia in the summer of 2016 but has failed to hit the heights with the Catalans.
The Spain striker scored just eight goals from 28 appearances in all competitions last term and has made only one La Liga start this season, with Ernesto Valverde clearly not a big fan.
Barca have now informed the hit-man that he is free to find a new club in the winter transfer window, according to Diario Sport, despite the fact he penned a five-year deal last year.
Palace tracked Alcacer last summer and may reignite their interest in mid-season to try and fight the battle against relegation.
Whether or not the player would be willing to join a club floundering in the lower reaches of the Premier League is another matter but a short-term deal might be on the cards.
Southampton have also been linked in the past and may challenge the Eagles for his signature should he leave Barca during the campaign.