Both Liverpool and Manchester United had been keen on securing his services after some very impressive performances for the Portuguese side.
However, Anzhi are set to dent their hopes as they are prepared to make a bid in excess of £20 million to lure the Argentinean to Russia.
Benfica are however set to do all they can to keep their star midfielder and would only accept a huge bid for him in the January transfer window, something that Anzhi look set to be preparing.
They have started the season flying in the Russian top flight and currently sit on the top of the table, so Gaitan is sure to be tempted with a move there.
He will also look at both Liverpool and Manchester United as huge clubs and a real chance for him to prove himself at the highest level.
The story is sure to keep changing between now and January, but it is certainly one to keep an eye on in the coming months.
Will it be Russia or the English Premier League for Gaitan?
We shall see.