Suarez trained with the rest of the Uruguay squad on Sunday ahead of Thursday's crucial Group D game in Sao Paulo and he looked in good shape and good heart.
The Liverpool striker - who underwent keyhole surgery on his knee last month - sat out his country's surprise 3-1 defeat to Costa Rica on Saturday and it remains to be seen if he will be considered fit enough to take on England.
The 27-year-old has cut a controversial figure in the past but played a crucial role in helping his club side to finish second in the Premier League last season to secure a return to Champions League action in 2014-15.
Suarez scored 27 times for Brendan Rodgers’ side but Hodgson is convinced he must impress at the World Cup before he can join the pantheon of world greats.
When asked whether Suarez belonged in the same "world-class" bracket as Lionel Messi and Cristiano Ronaldo, the England manager said: "I think he will only be at that level when he shows it on this particular stage.
"He has got the potential. He is he a wonderful footballer.
"But if you are really going to put him up there with (Diego) Maradona, Pele, (Franz) Beckenbauer and (Johan) Cruyff, and (Andrea) Pirlo, this is the stage you have got to do it on really.
"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."
Wayne Rooney is also in need of a good World Cup to prove himself as one of the best players on the planet.
The Manchester United player worked hard in the 2-1 defeat to Italy and supplied the cross which led to Daniel Sturridge’s goal.
But Rooney also spurned two good chances and is yet to score in nine finals appearances, with Hodgson keen for him to get into positions where he is more likely to find the target.
Hodgson cut a frustrated figure on the bench when Rooney, who started on the left flank, missed his best chance from 12 yards in the second half when he was played in by Leighton Baines.
"We want him in the area more," added Hodgson. "I thought he set up the goal really well with that clever pass.
"Then after Leighton Baines put him in with that pass I was convinced he was going to score when he got himself room in the box.
"But, yes, we want Wayne in the box and there's no question we will get him in the box."