The Spaniard was formally unveiled as the new man in charge four days ago having been out of a job since being sacked by Middlesbrough last March.
Along with Forest, a number of Premier League clubs are also looking at Musonda.
However, they will only do so if the Belgian is given first-team opportunities at Forest.
Forest are now 14th in the Championship, 11 points off the play-off positions.
Fresh from their excellent 4-2 FA Cup third round win over Arsenal before Karanka took over, Forest are next in action when they play Aston Villa on Saturday.