Manchester United have reportedly agreed to sell midfielder Angel Di Maria to Paris Saint-Germain for £44m, but they have already targeted a replacement.
This has surfaced after a long period of speculation that United would make a move for Gaitan.
The Daily Star reports that Gaitan is being valued at £22m, although a fee has not been agreed.
Louis van Gaal has been keen to bolster his midfield depth, and has already been proactive in the transfer window by signing Memphis Depay, Bastian Schweinsteiger and Morgan Schneiderlin.
Gaitan would mark the sixth signing of the summer for United. The Argentine international made 37 appearances for Benfica last season while scoring four goals.
He was also a part of his Portuguese club winning the last two Primeira Liga titles.
Arsenal & Chelsea combined XI: Blues outgun Community Shield opponents, Cech gets Courtois revenge
Man United 0-2 PSG video highlights: Zlatan STARS as Red Devils are outclassed by Ligue 1 giants
Celebrity football fans: PORNSTAR Man Utd lover, ROYAL Arsenal supporter & Chelsea-mad ACTOR in top 10