The Hungarian picked up the injury during his Tigers debut, last week’s 2-1 win at Nottingham Forest.
“He is not too bad, he is getting better,” said head coach Grant McCann at Monday’s open training session at the KCOM Stadium.
“In terms of timescale I am not sure, I don’t think the physios are sure so it’s how he responds.
“They have never dealt with Norbert being injured before, so it is new to them.”
McCann has not ruled out Balogh facing Fulham on Saturday. With Josh Magennis starting a four-match suspension, Tom Eaves was the only fit senior striker at home to Derby County.
“It is touch and go whether he will be right for Saturday,” said McCann. “We have to see how good his pain threshold is.”
Middlesbrough goalkeeper Darren Randolph could also return ahead of schedule after being named in the Republic of Ireland’s provisional squad for their Euro 2020 qualifier at home to Denmark.
Randolph’s club manager Jonathan Woodgate said last week he did not think the 32-year-old would be fit for the November 18 game, which the Irish are likely to have to win to qualify for next summer’s European Championships, but international boss Mick McCarthy has now said: “Darren is hopeful he will be fit to report in with the rest of the squad on the Sunday.”
Sheffield Wednesday’s Keiren Westwood provides cover in a squad which includes Sheffield United quartet David McGoldrick, John Egan, Enda Stevens and Callum Robinson, and Doncaster Rovers Kieran Sadlier.
Meanwhile, former Boro midfielder James Morrison has retired from football, aged 33. Morrison made 97 appearances for his first club.