The Argentina international has long been considered to be one of Portuguese football’s top talents and has been linked with a switch to Old Trafford in recent times.
However, Chelsea appear keen to win the race, with Jose Mourinho having had scouts in attendance to watch Gaitan during Benfica’s 5-1 win over Academica on Saturday.
The Blues look set to lose Mohamed Salah for at least another season to Fiorentina, so bringing in fresh options is appealing.
Benfica are known to be a side open to selling their most talented players for the right price, and bids of £30m are likely to be accepted in Lisbon.
Gaitan, 27, is a versatile attacking midfielder who is able to play in either flank or as a ‘No. 10’.