Tshimanga started his career at MK Dons when Neilson was manager and has been in red-hot form this season in the National League – English football’s fifth tier – with 19 goals in 23 appearances.
However, he is under contract until 2024. That means Tynecastle club would have to pay a significant fee for his services.
The Edinburgh Evening News understands that there has been no contact between Hearts and Chesterfield.
The player is also attracting interest from clubs in the English Championship and League 1 who have more financial muscle.
Tshimanga was a teenager when Neilson moved south and after several loan spells made a handful of appearances in season 2016-17 before dropping into National League.
The forward moved on to Boston United and a year later he found form at National League South Oxford City, scoring 37 goals in all competitions.
Boreham Wood and Chesterfield have benefited since with 60 goals across the last three seasons.
Hearts are still in the market for a forward to provide back-up to Liam Boyce, with Armand Gnanduillet expected to leave before the January transfer window closes and Jamie Walker having already gone to Bradford City.