The Frenchman, who has been a revelation since joining the Eagles on loan in January, was forced off against Tottenham last month with a knee injury.
Palace aren’t out of danger at the foot of the Premier League and face Hull and Manchester United still in need of points to rubber-stamp their top flight status.
Allardyce’s men host the Tigers this weekend in a crunch clash before a trip up to Manchester on the final day and the manager is pessimistic about Sakho’s chances of making either.
"Not really. I don't think so,” he said when asked. “It won't be long enough to think he'll be fit for Old Trafford."
Meanwhile Allardyce insists the "pressure lies on Hull" when they visit Selhurst Park for a fixture that could define each team's season.
Marco Silva's side could be relegated if rivals Swansea win at Sunderland on Saturday and Palace avoid defeat.
Allardyce had long believed 38 points - Palace's present total - could prove enough to avoid relegation but now knows that a draw against their under-threat opponents would guarantee it.
"The pressure lies on Hull. They have to win the game, we have to draw it," he said. "If we are defensively very sound and solid, like we were against Arsenal (in last month's 3-0 win), we are bound to create some chances at home and hopefully score.
"We play not to lose - that is the key element. It's been extremely difficult in the last three games. Hold your nerve on Sunday for one and make sure you produce your best performance and if that's good enough, then that's great.
"There is Hull we need to compete against, and the size of the game. Whoever deals with the pressure better is a big factor.
"Our crowd will be a big help as long as they get don't nervous. If they get nervous, they can pass that over and that will make us a bit more nervous. We have to deal with the emotion of the game on Sunday and come out on top.
"The clean sheet is all important. If we don't concede a goal, we stay in the Premier League.
"(The mental aspect of football) is one of the biggest parts of whether we succeed. Your football intelligence on the day decides whether you play well.
"Physically they are fit enough and if they hold it together mentally, stay positive and deliver the best performance, that will be good enough."
Allardyce will await the results of late fitness tests given to James Tomkins, Yohan Cabaye and Scott Dann before he selects his XI to start at Selhurst Park.Reuse content