The Rams have came close to promotion in the last two seasons, but they have failed to take the final step and make it into the Premier League.
However, Derby have made a very strong start to the 2015/16 campaign, and Barker claims they are on course to secure a top-two finish and hit their target.
“Everyone is looking at Derby at thinking they’re one of the stronger teams in the division,” Barker, who played for the Rams between 2009 and 2015, said. “They started quite slowly, and they were still finding their feet early on, but they have such a strong squad and a manager who has adapted quickly.
“We’re starting to see the best of the squad now, and if they don’t finish in the top two I’d be very surprised.”
Derby did begin their campaign in slow fashion, and they drew most of their early matches as they adjusted to Paul Clement’s methods.
However, they appear to have clicked into gear now, and they have managed to brush aside most of their challengers in recent weeks.
Derby have gone unbeaten through their last 10 matches, and this run of good form has elevated them into fifth place in the standings.
Derby’s next match comes against Nottingham Forest on Friday evening, and they know that a win over their local rivals will take them to the top of the table.