Liverpool, Chelsea and Arsenal all had the 21-year-old Spain international, who is valued around £15m, closely watched.
But any moves to sign him are set to fail with Alcacaer poised to sign a new five-year contract extension.
Football director Francesco Rufete said: "There are still a few minor details yet to resolve after months of negotiations.
"But everything seems to indicate that fairly soon we will be able to announce that Paco Alcacer will be a Valencia player for five years more [from his current deal]."
As part of the new deal, Valencia are hoping to increase the promising striker's buy-out clause, currently set at £15million, to £59million.
Alcacer has scored five goals and set up five more in 18 league appearances for Valencia.
