The Championship side have been linked with a deal for the Gambian, who plays as a winger, and belongs to Swansea City.
He is yet to break through for the Premier League side, and a loan deal would be wise for his development.
The paper claim Forest could make the move within days, in time for their weekend clash with Leeds United this weekend.
Barrow has one goal to his name since signing last September, a strike against Tranmere Rovers in the FA Cup earlier this year.
Forest loaned out central midfielder Robert Tesche last week to Birmingham City, who are paying his wages in full, freeing up funds for the Championship side to bring in a new addition.
They currently sit ninth in the table, but are still nine points off the play-offs despite losing only one of their last eight games in the division.
Forest beat promotion contenders Middlesbrough at the weekend 2-1, and loan signing Gary Gardner was one of the scorers, illustrating the impact a mid-season addition can have on the side.