Everton have impressed with their transfer dealings this summer, with Ronald Koeman strengthening his squad considerably.
The Toffees have made no secret of their desire to break into the top six in the coming years.
And Henry feels that Everton could have a chance of troubling the Premier League’s elite this term, if they bring in some more additions between now and the end of the transfer window.
“I would love him [Wayne Rooney] to do well,” Henry said.
“You hope that it's going to be a great Hollywood ending and he can help Everton win something.
“It looks like they are building a team there. If they get Gylfi Sigurdsson along with Rooney and maybe a few more, then the top six will have to watch out.”
Everton have begun their competitive campaign by progressing in Europa League qualifying, but their performance against their Slovakian opponents was not particularly impressive.
Everton will need to improve when the Premier League action starts up, if they are to live up to expectations.
Koeman’s side have a great deal of pressure on them to perform this term, and they will be looking to make a fast start.
Everton begin their campaign at the weekend, when they take on Stoke City at Goodison Park.