The Manchester United forward has been in terrific form for his country, scoring in their last two World Cup qualifiers to take his tally to seven goals in his six games in the campaign as England finished top of their group.
However, the 27-year-old's performances at past major tournaments for England have been less than stellar.
Rooney, who played in the 2006 and 2010 World Cups, has yet to find the net at the finals and has a less than perfect overall disciplinary record in internationals, having twice been sent off.
"If the question is, do I believe Wayne Rooney has got the ability and can be a star at the World Cup playing for England playing like he is at the moment?, I would say: 'Yes of course I believe it, of course I think he can do it'," said Hodgson at a media briefing this week.
"You can't keep judging people on the past and errors they've made in the past. If there's been temperament errors, he's been lambasted for them and paid the penalty for them but you can't keep on dragging that up," added the 66-year-old.
Rooney was infamously sent off against Portugal in the quarter-finals of the 2006 World Cup after stamping on Ricardo Carvalho and pushing his then-United team mate Cristiano Ronaldo.
England lost the match 3-1 on penalties to go out of the competition.
Four years later in South Africa, Rooney drew criticism after sarcastically commenting to television cameras "nice to see your home fans booing you" as he walked off the pitch at the end of a lacklustre 0-0 draw with Algeria in a group game.
He later apologised for the incident.
Rooney was also shown a straight red card in a Euro 2012 qualifier against Montenegro for petulantly kicking out at Miodrag Dzudovic and missed the first two matches of the tournament.
Hodgson intimated he wanted to let bygones be bygones as far as Rooney was concerned and cited the forward as being a shining example to the younger squad members.
"If we look over the last 10 games we've played in these qualifying tournaments ... his discipline has been fantastic," the manager said.
"His discipline around the place, his influence and his example to the other players, I can only judge like that. I'm not really prepared to concern myself with 'well in this tournament this, or in that qualifier that'.
"I'm only prepared to judge Wayne on how he's been with me since I've known him and he's been very, very good both as a player and in terms of his discipline so why should I doubt him?".
After a sometimes less than convincing World Cup qualifying campaign, England ended with a flourish with dominant performances against Montenegro and Poland to finish unbeaten.
Rooney was prominent in both matches and while Hodgson has played down England's chances of winning the trophy he is content with the way his team played.
"I would like to think the footballing public have been satisfied with us so far and have even got a certain degree of excitement with the players we've got coming through now and the way we're trying to play," he said.
"This could be an interesting tournament."