Boucaud spent five months on loan at Meadow Lane after being told by the Hatters that he had no future at the Blue Square Bet Premier club.
The 28-year-old midfielder made 23 appearances for the Magpies, the last of which came in the 2-1 defeat to MK Dons on New Year's Day, and manager Keith Curle has made no secret of the fact he would like to sign Boucaud.
A statement on the club's official website said: "Notts County Football Club is currently in transfer negotiations with Luton Town and Andre Boucaud with the hope of bringing the player to Meadow Lane on a permanent basis.
"The Kenilworth Road club has requested a fee for the midfielder.
"First-team manager Keith Curle would like to keep hold of Boucaud, but until a deal can be struck he will remain a Hatters player."
