The Sunday Telegraph reports that United are set to agree on a £29.3million deal to sign the midfielder at the end of the season.
Benfica have reportedly struck an informal agreement with United over the sale of the highly-rated midfielder.
Gaitan has impressed for Benfica in the Champions League this season and could fill the void left by Paul Scholes at Old Trafford.
Gaitan joined Benfica from Argentine side Boca Juniors in 2010.
