The 26-year-old was sidelined for three weeks after the autumn international break, and he was forced off in Liverpool’s 3-1 Premier League win over Crystal Palace before joining up this time around.
Andoni Iraola was unconvinced over his readiness to head away with his country, but after extensive tests by Hungary's medical team, he remained with them.
The Reds' No.8 was named in the starting line-up for Hungary's 2-0 UEFA Nations League win in Georgia on Saturday, where he claimed a second-half assist.
However, ahead of kick-off, Szoboszlai admitted he was considering pulling out after an injury flare-up.
"I came today with a workout and a half in my legs. In the warm-up, I was close to saying no, because I felt my leg on one of the shots.
"But if I've come this far, I won't let the team down. I went as best I could, trying to give my best."
Szoboszlai will undergo further treatment ahead of Hungary's final game at home to group leaders Northern Ireland on Tuesday.