Clyne's strike in a 2-1 win at Arsenal on Tuesday secured the Saints passage into the fourth round.
The 23-year-old has been overlooked by Three Lions boss Roy Hodgson thus far, despite impressing since joining Southampton from Crystal Palace in 2012, but his club manager Koeman is positive that Clyne has what it takes to be an asset for his country.
"I think he's ready," he told reporters. "He has a lot of experience, he is playing very well from the beginning of the season.
"He scored a great goal. I think his performance was very good and I think it's an option for the national coach and I'm very happy to have Clyney in our team because he brings a lot of experience.
"He brings a lot of spirit and I like to have and play with offensive full-backs. He shows that quality and it's very important for the team."