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England coach Hodgson and his side could face Liverpool striker Suarez on Thursday, although doubts surround his fitness after he was an unused substitute in Uruguay's opening 3-1 defeat to Costa Rica.
The striker scored 27 goals as Liverpool finished Premier League runners-up last season, and Hodgson feels he must replicate that level of performance in Brazil in order to be considered one of the greats.
"He will only be at that level when he shows it on this particular stage," the coach told reporters. "He has got the potential -- he is a wonderful footballer.
"But if you are really going to put him up there with [Diego] Maradona, Pele, [Franz] Beckenbauer, [Johan] Cruyff, and [Andrea] Pirlo, this is the stage you have got to do it on.
"You can be a great player in your league, but for the world to recognise you are one of the all-time greats you have got to do it at the World Cup."
Having told his Liverpool teammates in the England squad prior to the tournament that he would play against them in Sao Paulo, Suarez has now gone silent, according to his Anfield colleague Steven Gerrard.
"I'm not sure where Suarez is up to injury wise, but I expect him to play some part because he's been so quiet," the England skipper said. "I expect him to be involved in some capacity.
"They [Uruguay] have really good firepower up front -- but we've seen against Costa Rica that they are certainly beatable. They concede goals, and if we attack like we did against Italy we will cause Uruguay big, big problems."
Expect the unexpected with Suarez
Former professional referee Peter Walton explains that great players like Luis Suarez are very unpredictable and difficult to officiate.
#WorldCupRank: 4 - Luis Surez
Luis Suarez will be looking to guide Uruguay to another triumph in Brazil after a phenomenal season with Liverpool.