The Sun says Neville has been working in the media since hanging up his boots – apart from a disappointing spell as coach alongside brother Gary at Valencia.
But now he is set to swap the TV studio for the dug-out by taking over at Gigg Lane in an effort to revive the League One club's fortunes.
Bury sacked David Flitcroff last week and the club's chairman Stewart Day is desperate to bring in Neville, 39, to help turn their season around.
And the lure of taking over at the club which is so closely linked to the Neville family is one that is proving hard for the former Everton and England star to turn down.
An insider said: “To have Phil here in charge would be marvellous and hopefully pull our season around."