The Hungarian is on a month-to-month contract with the cash-strapped South Coast club, who are currently two places from the foot of the League One table and still in administration after nearly a year.
A former international, the 31-year-old arrived at Fratton Park on a free transfer last summer following spells with Wolves, Northampton Town and Cardiff City.
"My contract theoretically expired on 5 January, but I decided that - until I have another challenge - I'll try to help the team and of course I'll try to stay in shape," he told skysports.com.
"I signed another one-month contract, we agreed about it with the club in case of an offer I'm allowed to leave."
Portsmouth's predicament saw Gyepes sit on the bench despite an injury sustained at Christmas.
"I had a tear in a hamstring in our game on 26 December so I was sidelined," he added, "but I had to sit on the bench against Walsall because we don't have a big squad.
"I'd like to stay because it's a big club, with great expectations, I feel really good here and my family would like the life here too. But the state of the club, and these one-month contracts would sooner or later urge anyone to think it over and look for another job."