The 26-year-old was injured during the last international break and was forced off in Liverpool’s 3-1 Premier League win over Crystal Palace at the weekend.
The midfielder was withdrawn on 69 minutes against the Eagles due to a knee problem, in his first Premier League start since returning from a hamstring injury, and Andoni Iraola offered a downbeat update at full time.
"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 have since confirmed their captain will undergo checks with their medical staff before a decision is made on his involvement.
Hungary wrap up their UEFA Nations League campaign away in Georgia on November 14 before hosting Northern Ireland three days later.