The likes of Falcao and Robin van Persie left United earlier this summer and Javier Hernandez is expected to leave Old Trafford before the transfer window closes.
“In terms of Manchester United and bringing a striker in before Deadline Day, they needed a striker when Welbeck went,” Carragher told Sky Sports.
“Not necessarily straight away, but as soon as Welbeck went, with the age profile of Falcao, Rooney and Van Persie, it was obvious in 12 months’ time they were going to need a 23, 24 year old striker to come in.
“The only other option is Fellaini to come in as a centre forward if Rooney was out. He was playing as a holding midfielder at Everton, so it’s certainly an area they’ll need to look at.”