Ramsey is believed to have agreed a deal with Juventus to join them at the end of the season.
The 28-year-old is departing the Emirates after Arsenal withdrew a contract offer in September.
With his future uncertain Ramsey has been a substitute for much of the season under manager Unai Emery.
But the Wales star may have forced himself in Emery’s plans after an impressive performance against Chelsea in the Premier League on Saturday.
And Koscielny has hailed Ramsey’s professionalism and says he expects full effort from the midfielder.
“He shows great character every day in training and when he plays. He gives 100 per cent which I respect a lot,” he told Sky Sports.
“Sometimes players just think about themselves before the club, but he is a very good professional.
“He will give 100 per cent for the club until the end.”
Meanwhile, Koscielny has leant his support to Hector Bellerin, who will miss the rest of the season after rupturing his anterior cruciate ligament against Chelsea.
Koscielny has only recently recovered from an Achilles injury which put him on the sidelines for seven-months.
But Koscielny handed his team-mate some advice on how to deal with a long-term injury.
He added: ”Like I said to him yesterday, put football on the side and enjoy a bit of your life with your family and friends.
“He is starting a new chapter of his career.
“It will be long but he is a strong boy and I know he has the people around him to help him and be back as soon as possible and stronger than before.
“He knows all the team are here to help him because we know he will have some difficult moments during his rehab, like Rob [Holding] and Danny [Welbeck], but they know all the team are here and behind them to help them come back with us and help us to have results together.”