The report claims the West London club are eyeing the talented winger in a £1.5 million deal, although they can only press ahead with their interest once their current transfer ban has been lifted.
Marshall began his career at Manchester United as a youth player before having spells at Crewe Alexandra under Dario Gradi, Stoke City, Leicester City and now Blackburn Rovers.
The England under-21 international has been in and around the Championship for the past few seasons, impressing while on loan at Sheffield Wednesday before joining Rovers in 2013.
Capable of playing both at full-back and on the wing, Marshall enjoyed his best year last season where he managed to score six goals and add a further seven assists in 42 Championship matches.
This season has not been quite as productive for the 24-year-old, with Gary Bowyer’s sacking as manager midway through the campaign disrupting his progress somewhat.
Rovers have not enjoyed a particularly good campaign, and the same can be said of Fulham who currently sit just above the Championship’s bottom three.
Having said that, the Craven Cottage side do boast a number of quality players and in Slavisa Jokanovic they have a manager who knows how to win games in the second tier.
Fulham are expected to be much better next season, and with Marshall in their ranks they could have the ideal winger to supply the ammunition for top scorer Ross McCormack.