The Turkish giants are keen to bolster their attacking options and have identified the out-of-favour Argentine as the perfect addition to the squad
The diminutive forward has been strongly linked with a move away from Benfica in January after a disappointing start to his third season at the Estadio da Luz.
Saviola's contract runs out at the end of the season and the Portuguese giants have yet to state whether they will exercise their option to extend the Argentine's deal by one year.
The 29-year-old had already been on Galatasaray's wishlist during the summer transfer window, but a move failed to materialise.
The former Barcelona man, who joined Benfica in 2009, has scored 36 goals in 104 appearances for the Portuguese side.
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