HITC Sport understands Sheffield United reject bid for defender.
Northampton boss Jimmy Floyd Hasselbaink is looking to bring in a new central defender before the close of the transfer window and had targeted a move for Heneghan.
However, United have turned down Northampton's offer to sign the player on a permanent basis, and it means Hasselbaink will now be forced to look elsewhere in his hunt for a new defender before next week's transfer deadline.
Heneghan has struggled to make an impact at Bramall Lane since joining the club from Motherwell last August.
The 24-year-old has yet to make a single first-team appearance for the Blades, as he has been unable to break into Chris Wilder's plans with Sheffield United riding high at the top end of the Championship.
Heneghan moved to Motherwell in 2016 from non-league Chester and he made an instant impression in Scotland with a number of clubs chasing him before Sheffield United won the race for his signature.
It remains to be seen if former Everton and Stoke youngster Heneghan will move elsewhere before the close of the transfer window.