Barnsley chairman Peter Risdale said: "We have today stepped up our search to bring in a new striker and have today been given permission to speak to one player.
"We intend to hold talks with the player tomorrow."
Stallard is one of Notts' biggest fan favourites in the last 10 years, almost single-handedly keeping the club in the Second Division last season with 25 goals.
This season, however, he has only fired in 6 goals and has looked badly off colour of late. Despite this, it would still be devastating for Notts' fans to lose a player who genuinely loves the club.
NCM will keep you updated when/if this moves goes through.