Zaki joined the Latics in the summer on a season-long loan from Egyptian side Zamalek.
Bruce has confirmed reports that they had agreed a £7.25million fee for Zaki, but they decided not to go ahead with the move.
Wigan will now face competition, to sign him on a permanent deal, from several clubs for the Premier League top scorer in January.
“I want to put the record straight because, at the minute, everyone wants a piece of the fellow. The truth of the matter is he’s on loan with us until June. That’s a fact,” Bruce told The Guardian.
“Over the next few weeks, or however long it takes, we will try and open negotiations with Zamalek and do everything in our power to try and make sure he stays here.
“Zamalek were hoping, and that’s why they took the deal, that he would do well. Obviously, the better he does, the bigger the fee. He’s our player, so we’re in the driving seat.
“We haven’t got first refusal on anything. But we have got to see if we can agree a transfer fee with Zamalek.
“Of course, with hindsight, it would have been nice for him to have been ours. But we have still got a chance – that is the most important thing – and we will do our utmost.”