The midfielder is valued by the Portuguese side at 30 million euros, having attracted the interest of Sir Alex Ferguson when the sides met in the Champions League.
But Manchester City have also shown an interest after watching the 23-year-old during Benfica's win over Maritimo last week.
Benfica are bracing themselves for offers when the transfer window re-opens in the summer and hope to raise 50 million euros in all of their dealings.
Club president Luis Filipe Vieira said: "The sale of players is the priority for Benfica but only if it is helping the club.
"Our aim is to break even and make around 50 million euros in the summer through sales."
It is understood that Benfica coach Jorge Jesus has been told that Gaitan is to leave in the summer.
They are also expecting to lose Paraguay striker Oscar Cardozo and Argentina defender Ezequiel Garay.