The former midfielder has backed them despite disappointing defeats to Manchester United and Arsenal in recent weeks.
The Blues currently sit tenth in the table after a solid start to the campaign, but suffered their first away defeat of the season on Saturday as they were beaten 2-1 by Arsenal at the Emirates.
That was the second straight defeat after they lost to Manchester United last weekend as well, in what has been a tough run of games for them with them facing Liverpool before the international break.
They have faced all of last season’s top seven in their first ten games, with a series of very winnable games coming up, and Murphy has backed them for a top six finish.
“They’ve lost to some quality opposition lately and lacked that quality themselves,” he told Match of the Day.
“But you would suggest their games coming up now give them a better opportunity, I still expect them to finish in the top six.”
Can Everton reach the top four this season?
There is no denying that Everton certainly have the quality to finish in the top six this season, but getting beyond that is likely to be a struggle.
The squad that Roberto Martinez has is full of quality in all areas, while he also now has options from the bench when he needs to use them.
The recent losses to Arsenal and Manchester United have however indicated that they may not have that extra quality to reach the top four though, meaning a place in the Europa League next season could be the best they can hope for.