The Eagles signed Sakho on loan from Liverpool during the January transfer window and the France international has helped Palace turn their season around.
Palace kept just two clean sheets in 25 Premier League matches before Sakho was brought into the side, but the south Londoners have conceded only twice in six games since his debut.
Allardyce confirmed on Friday the loan agreement does not include a clause to make the move permanent, but suggested Palace will make a move for the Liverpool defender once his side are mathematically safe.
"[There is] no clause to make Mama's stay permanent, but it was a great deal getting him in," said Allardyce.
"We can't talk about 'that' until we're safe."
Sakho was frozen out at Liverpool before securing his temporary move to Palace.
Indeed, the central defender had not featured in a senior match since April 2016 when he first appeared in Palace's red and blue in February.
But Jurgen Klopp refused to be drawn on Sakho's Liverpool future on Thursday.
“I see a lot of Premier League games so I see Crystal Palace too and I see how he is playing there and all this stuff," said Klopp.
“But there is nothing to say in this moment because you can imagine like all the plans we have for next season, we speak about behind closed doors. In the moment when we have to say something we will say something.”