Forest need an extra forward after the season-ending injury to striker Britt Assombalonga, and it's believed that Barrow could join on loan until the end of the season.
Barrow is far from a household name in the Football League, so here are five things Forest fans should know about their reported transfer target ahead of his possible arrival at the City Ground.
- Barrow, 22, joined Swansea City last summer after a lengthy career in Sweden, playing for the likes of Mjolby, Norrkoping, Varbergs and Ostersunds.
- After ten goals in 19 games for Ostersunds, Barrow earned his move to Swansea - who fought off interest from Bolton Wanderers to sign him, who were of course managed by current Forest boss Dougie Freedman at the time.
- After making his Premier League debut against Arsenal back in November, Barrow bagged his first Swans goal in the 6-2 FA Cup win over Tranmere in January, also bagging an assist in that game.
- Barrow stands at just 5ft 9in tall, but possesses superb pace and can play either out wide - preferably from the right hand side so he can cut in on his left foot - or up front, which will certain help Forest in their pursuit of a play-off place.
- At international level, Barrow has yet to commit his future to a nation. Eligible to play for both Gambia and Sweden, Barrow hasn't made his mind up yet - but it surely won't be long before he's representing one of them.