The midfielder was forced to withdraw from the Republic of Ireland squad for next week's friendly international with Wales in Cardiff.
Pilkington is also doubtful for the opening Premier League fixture against Everton on 17 August but Hughton is keen for him to return to action soon.
"We are just managing a slight problem with his knee at this moment in time," said Hughton.
"Anthony did the first part of pre-season and he did very well but when it came round to these most recent period of games we have not been able to use him.
"We are hopeful that he is going to be training next week and to push on from there."
City centre-back Sebastien Bassong is also an injury concern, having missed the whole of pre-season following an operation on his knee.