Sky Sports understands several Championship sides and Scottish giants Celtic are keeping tabs on highy-rated centre back Morrison.
The 25-year-old is out of contract at the end of the season and as yet there has been no new offer of a new deal at Charlton.
The news has alerted a host of sides to Morrison's possible availability with the 25-year-old establishing himself as one of the best defenders outside the Premier League.
The former Leicester City and Sheffield Wednesday man has already made over 300 appearances in his career and is vice-captain at Charlton.
Charlton are thought to be keen to keep Morrison, but could find their resolve tested this month as his suitors weigh up moves for the player.