The Lilywhites have been reported to have turned down bids from Birmingham, Wolves and Reading for Hugill, who put his desire to leave Deepdale in writing earlier on Tuesday.
“Preston North End can confirm that Jordan Hugill has (on Tuesday) handed in a written transfer request,” the club said in a brief statement on their official website.
“The club have rejected this request and will not be selling him in this transfer window.”
Wolves and Reading are understood to have had bids of around £8million turned down last week, while Leeds and Sunderland have also been linked with the 25-year-old.
Preston boss Alex Neil, appointed in July following Simon Grayson’s departure to Sunderland, insisted on Monday that Hugill was not for sale.
Hugill, who joined Preston from Port Vale in 2014, signed a new two-and-a-half-year deal in October 2015.
He scored 12 goals in the Championship last season and has scored three in six games in all competitions this campaign.