Gerrard started out his spell as Aston Villa manager on a positive note when his side beat Brighton 2-0 last weekend.
The new Aston Villa boss has been planning for the winter transfer window and wants to bring in fresh reinforcements in the middle of the season.
Gerrard is expected to be backed by the club and has identified left-back as a pressing area of concern, with Sosa a target.
According to German daily Bild, the new Aston Villa manager wants to take Sosa to the Midlands in the January transfer window.
He wants more options at left-back in his Villa squad and believes the 23-year-old Croatian will suit his needs.
It has been suggested that Aston Villa are prepared to put in an offer of €30m to snare Sosa away from Stuttgart in the middle of the season.
The German club are likely to be receptive to such offers as they recently revealed losses to the tune of €80m.
A big-money offer from Aston Villa could force them into selling Sosa due to financial considerations.