Manchester United forward Rooney claimed his 42nd international goal on Thursday as England eased to a 5-0 victory over San Marino at Wembley in their latest Euro 2016 qualifier.
Rooney, who turns 29 later this month, is now just seven goals short of the England record held by Bobby Charlton.
Hodgson expects his captain to surpass Charlton's mark of 49 and played down the fact Rooney missed a number of chances to add to his tally against San Marino.
"The record won’t play on Wayne's mind," said Hodgson.
"We'd like to think, with the way he is and the footballer he is, he's got a good few years in him yet.
"There are plenty of games left. I don't think we should put any pressure on him to reach targets early."
Rooney will have the opportunity to move closer still to Charlton when England, seeking a third win from as many games in Group E, face Estonia in Tallinn on Sunday.
