The Irons head to Manchester City on Sunday without their 12-goal frontman, who limped off against Stoke last weekend.
Sakho, impressive in the early part of the season following a summer move from Metz, now faces a race to be fit for the final matches of the Barclays Premier League campaign, but will not be rushed back into action.
Allardyce is already without England forward Andy Carroll following a knee injury, although Enner Valencia has shrugged off a foot problem to play, so is banking on veteran striker Cole, who has just three goals this season, to produce a vintage display at the Etihad Stadium.
"It leaves us very short in goalscoring options, but I am expecting that Carlton will come in and play a big (role) for us in the next few games with the performances like we know he can," said Allardyce.
"It is a thigh injury (for Sakho), we think maybe towards the end of the season (he could be back), but maybe not.
"You have to be very careful with a thigh strain, so that he does not get a recurrence.
"If he is fit, he is fit
We would say 100 per cent fit, and not want to risk him if he was 95 per cent fit, we would give him that time to be absolutely certain, which would mean we would have to be at least four or five days training with the rest of the squad before he was available."
Premier League champions City have seen their title defence left in tatters following a run of four defeats in six matches - which includes last weekend's 4-2 defeat at city rivals United.
Allardyce is hoping his side can raise their game, following the disappointment of conceding another stoppage-time goal as Stoke earned a 1-1 draw at Upton Park last Saturday
"Like ourselves, they cannot find a way to win at the moment," said the Irons boss
"It is one which is going to test their nerve a little bit and hopefully we can test their nerve
"But at home, they have been very good, it will be tough, hard to get something.
"By the way they started against Manchester United, you thought it would be a turning point for them, but at the end of the game, it was United who deserved to win."
City's poor form has seen the long-term future of manager Manuel Pellegrini in some doubt as they might now face a scrap with Liverpool for a Champions League qualifying spot
German coach Jurgen Klopp has been installed as the bookmakers' favourite to become the next City manager following the announcement he was to leave Borussia Dortmund in the summer.
Allardyce would like to see some more home-grown managers get a chance at one of the Premier League's leading clubs.
"There should always be hope for British coaches, we are very good at what we do and you get tested at every level of your ability," said the Irons boss, himself not yet having sorted his own future past the end of the season.
"We enjoy the club you manage and try to get success where you can, then whatever will be, will be."
Source : PA
Source: PA