Forlan has been a target of Man. United and West Ham in recent weeks but sources in Argentina suggest that his club Independiente have agreed a £6.5m fee with Boro.
The club admitted today that they were interested but that there was no deal imminent.
The 22-year-old has interested a number of clubs across Europe after netting 18 goals last season in 34 games, he has scored 12 so far this season in just 18 starts.
Boro have also shown an interest in Norwegian Andre Schei Lindbaek who has started a weeks trial with Boro.
The former U-21 international is currently in the close season with Molde, for whom he scored 10 goals last season.
Boro may be losing out in the race to sign Dwight Yorke from Man. United, it would seem that Sunderland are now favouites to sign the unsettled striker.