The Sunday Mirror says United want Guardiola to succeed Ferguson.
United have asked the 41-year-old Spaniard to keep them informed of his future intentions following his decision to quit Barcelona.
Chelsea have led the chase for Guardiola and owner Roman Abramovich wants him to oversee the next stage in their rebuilding.
But Guardiola’s also receptive to the idea of following in Fergie’s footsteps at Old Trafford.
And there have been suggestions that Ferguson could finally call time on his glorious career at the end of next season.