The Brazilian, who won the tournament as a coach in 1994, feels the Three Lions squad has enough quality to go all the way - but only if they navigate out of Group D
Roy Hodgson's side have been drawn against Costa Rica, Uruguay and Italy - who eliminated them from Euro 2012 on penalties.
England have failed to get past the quarter-final stage of the World Cup since 1990, with many tipping them to fall at the first hurdle in Brazil later this year.
And, though Parreira - who won the tournament in 1994 - concedes the group will prove tricky, he believes they could challenge anybody in the tournament should they emerge from their pool.
"The group is very tough ... nobody can say right now who is going to survive in this group," he said.
"If [England] survive they can go very far in the competition. We played them twice, we lost one and we drew the second one.
"The team is very good, I rate them as one of the favourites together with Spain, Brazil, Uruguay, Argentina, Germany."
Parreira highlighted captain Steven Gerrard as England's star performer, and believes the Liverpool man would command a place in Brazil's midfield.
"I like Gerrard very much; he is, for me, a wonderful player," he added. "He would play in the Brazilian team, yes. The Brazilian players love him, respect him."