The 26-year-old centre-back is out of contract at Home Park, but has recently been offered a new contract at the Pilgrims.
The Hatters were reportedly keen on signing Bradley in last summer’s transfer window, but had a £250,000 bid rejected by Argyle.
Nathan Jones’ side were the biggest spenders in League Two last season, and it paid off after their impressive campaign saw them finish runners up, behind Accrington Stanley.
Sonny Bradley, who played 44 times in all competitions for Plymouth Argyle this season, has caught the eye of other clubs too, with Scottish clubs Rangers and Heart of Midlothian also linked with the former Crawley Town, Hull City and Portsmouth man.
Sonny Bradley would be a real loss for Plymouth Argyle, but whether the Pilgrims can compete financially with Luton is still to be seen.
The young defender has already racked up seven clubs in his short career so far, so the Hatters will be hoping to get Bradley tied down to a long term deal at Kenilworth Park.
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