The 26-year-old was sidelined for three weeks after the last international break and he was forced off in Liverpool’s 3-1 Premier League win over Crystal Palace last weekend.
The midfielder was withdrawn on 69 minutes against the Eagles after flagging up a knee problem, in what was his first Premier League start since returning from a hamstring problem, and Andoni Iraola was unconvinced over his readiness to head away with his country.
"The last thing we need now is to lose players in the international games.
"In the last international break we lost three very important players in Isak, Gakpo and Dom. So, I'm praying - it's the last thing we need.
The Hungarian Football Federation confirmed their captain has undergone several tests on the injury with their medical staff, but they are confident he can remain in place for the UEFA Nations League double header against Georgia and Northern Ireland.
"Dominik Szoboszlai has undergone the required medical examinations. Following a knee sprain, the national team’s medical staff will do everything possible in the coming days to ensure the team captain is available to the coaching staff as soon as possible.
“However, a decision on his availability for the matches will almost certainly only be made at the last minute."