Manchester United are enduring their worst start to a season in 30 years under Ole Gunnar Solskjaer, with the club winning just two of their eight league games so far this season.
The Red Devils are 12th on the table, just two points above the relegation zone and could slip into the bottom three if they lose to leaders Liverpool in their next Premier League game after the international break.
The club’s poor form has not been helped by injuries to key players at the early stages of the campaign.
Of the eleven players who begun the 4-0 opening day win over Chelsea, only five were present from the start against Newcastle last Sunday as the likes of Paul Pogba, Anthony Martial, Luke Shaw and Aaron Wan-Bissaka were all serving time on the treatment table.
Manchester United were famously relegated from the old first division in 1974, just six seasons after winning the European Cup, and Allardyce fears the same thing could happen if things do not improve.
"They went down [in 1974] with a terrific team on paper," Allardyce told talkSPORT.
"So it isn't beyond the realms of possibility that they could catastrophically fall into more problems if confidence goes and injuries stay like they are.
"Players tend not to get as fit as quick as they would do when things are going well, that's an absolute fact.
"There's the disturbance of [Paul] Pogba wanting away and who will pop up next saying, 'I see this going the wrong way, I want to leave?'"
United have struggled for goals this season, failing to score more than once in a game since that opening day win over Chelsea, and Allardyce believes Solskjaer erred in not replacing Lukaku, who was their top scorer for the last two seasons, after he left for Inter Milan.
"Manchester United do not have enough goals and you can see it becoming a struggle. Hopefully it's not a struggle down the bottom end, but they're certainly heading that way." he said.
"Ole's got a big job, I know they say it's a rebuilding time and it is a rebuilding time, but you can't get rid of your best goalscorer in the squad and not replace him. That's a huge problem.
"Where are they going to get the top striker that they want?"
