The new Hammers boss expects to lose England internationals Scott Parker, Robert Green and Carlton Cole, with the latter a target for Stoke, while 11 of last season's squad have already left Upton Park.
"That has helped the financial fall-out of being relegated but now, unless there are four or five of the young players ready to come in, we probably need to sign eight from outside," Allardyce told the Evening Standard.
On his England trio, he added: "The three of them will all probably all want to go to clubs in the Premier League if they can. We will just have to see how things develop."
Allardyce, who has already brought in Kevin Nolan and Abdoulaye Faye, has handed trials to Brazilian defender Hernani da Rosa and former Bolton midfielder Joey O'Brien for the squad's pre-season trip to Switzerland.
He has also appointed former Barnet manager Ian Hendon as the club's development coach.