"We are full of confidence," Koeman told Southampton's official YouTube channel.
"Of course, we know we have some difficult ones (games). That starts this Sunday. Leicester are playing for the title and that will be a very tough one, but we are Southampton.
"We can make it difficult for all the teams and we have a good record against good teams."
Before the international break, Koeman's side recovered from 2-0 down to win 3-2 at home to Liverpool, giving them seven victories and two draws in the past 11 games.
"We had a great win against Liverpool and if we show the same spirit and same quality as we showed in the second half then we can get a good result," the Dutchman said.
"...they (Leicester) are also afraid of Southampton because they know we can beat everybody."
Saints may have to do without Shane Long, however, after the striker was injured playing for Ireland.
Left-back Ryan Bertrand is fit, despite withdrawing from the England squad, as are forwards Charlie Austin and Jay Rodriguez, who have recently been out with injuries.
"It's important to have everybody available for the last seven games," Koeman added. "It starts on Sunday with a fantastic game, and we are looking forward to it."
(Reporting by Steve Tongue; Editing by Ken Ferris)
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