The right-back moved to Ibrox during last summer's transfer window but has appeared just once under new Rangers boss Pedro Caixinha.
Celtic's Kieran Tierney (right) in action with Rangers' Lee Hodson
Hodson arrived at Ibrox during last summer's transfer window, but has made nine league appearances all season and has played just once under new Rangers boss Pedro Caixinha.
Though a full Northern Ireland international, Hodson was born in Hertfordshire and a move to Charlton could appeal, especially with the 25-year-old having played under Addicks boss Robinson at Milton Keynes Dons last season.
As well as the Rangers man, Charlton are also said to have lined up moves for MK Dons' Ben Reeves and Bradford City pair Mark Marshall and Billy Clarke, who are managed by former Ibrox favourite Stuart McCall.
Charlton Athletic manager Karl Robinson (left)
This will be Robinson's first summer window in charge of the League One side, who ended their first season back in the third tier in 13th place on Sunday.
Hodson's Rangers contract still has another two years to run, meaning the Gers will likely demand a fee for the former Watford trainee.
Should Rangers allow Hodson to leave Ibrox?