The Eagles shocked the Premier League last week as they parted company with Tony Pulis, who had saved them from what looked to be certain relegation last term.
Since then a number of names have been linked with the role, but Sherwood is understood to be the favourite.
The 45-year-old was sacked by Tottenham at the end of last season after less than six months in charge of the club, and is thought to be desperate to get back into management.
He will bring former assistant Les Ferdinand with him if he is given the job.
Malky Mackay is also in the running, with the former Cardiff chief reportedly using the influence of figures such as Sir Alex Ferguson to bag the position at Selhurst Park.
Chris Hughton of Norwich is another name in the frame, while ex-Celtic gaffer Neil Lennon has been aligned with the vacant position.