North End made an contact with their league rivals following the sacking of Phil Brown in December.
"Stevenage FC confirm that Preston North End FC have asked for permission to speak to Graham Westley with the view to employing him as their new manager," read a statement on the club's official website.
"The club have informed Preston that their approach is unwelcome at this crucial stage of the season. However, as always in these situations, the manager's desire will influence the outcome."
Westley was appointed Stevenage boss in 2008.