The 22-year-old, who became the first Gambian to play in the Premier League when he made his debut in a 2-1 victory over Arsenal in November, forced his way into the Swansea first-team squad after arriving from Swedish second-tier Ostersunds during the close-season.
However, manager Garry Monk's new-found preference for a narrower formation, which has seen experienced wideman Nathan Dyer left out of the matchday squad for the last three matches, restricted the opportunities afforded to Barrow.
Barrow last featured in a 1-1 home draw against Sunderland on February 7, but will be hoping to make his Forest bow at Leeds United in the Championship on Saturday.
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