The Republic of Ireland captain sustained a double leg break in Friday night’s World Cup qualifying game against Wales in Dublin.
Koeman said: “I haven’t been able to speak to Seamus as yet and I hope to do so this afternoon, but he will be aware that the thoughts of his teammates, the coaching staff, everyone at the Club and all Evertonians are with him at this time.
“No-one ever wishes to see something like this happen to any player, much less one of our own.
“The medical staff here at Everton are in contact with the medical staff of the Republic of Ireland and we will continue to liaise closely.
“Seamus will face a lengthy recovery period and we will support him throughout this.
Former Everton team colleague Leon Osman said: “I’m absolutely gutted for him. I wish him all the best and a speedy recovery.
“Knowing him, though, he’ll come back better, fitter and stronger. That’s the type of character he is.
“He was playing for Sligo Rovers in the Irish league when he was 20 so he’s got a real appreciation for the game. He’s a real nice, genuine lad – he doesn’t carry any of the arrogance a lot of footballers have.
“I’ve got all the time in the world for him. He’s one of the genuine nice guys in football. It’s upsetting it’s happened to any player, never mind such a top guy in Seamus.
“Seamus is the type of guy who will be devastated but he’ll work his socks off to get back as quick as he can.
“Watching the game, the moment it happened, Evertonians were devastated to lose such an influential character – he’s a future captain of Everton Football Club. It’s a big loss and everyone felt it.
“Everyone loves Seamus and will be desperate to get him back as quickly as he possibly can.”
On Sky Sports Sunday Supplement programme this morning, The Mirror’s Chief Sports Writer Andy Dunn described Taylor’s tackle as “totally wreckless.”
The world of football has been horrified at the injury and Twitter has been full of tweets of support Seamus:
Coleman’s Everton team-mate Ramiro Funes Mori:Devastated of what happened. Hope you have a speedy recovery my friend, best wishes for you. You will come back even stronger!!! SeamusColeman.
Arsenal right-back Hector Bellerin: Get well soon @seamiecoleman23!! #RightBackUnit
Irish 20-time champion jockey AP McCoy: Gutted for Seamus Coleman. Hopefully he’ll have speedy recovery
Actor and television presenter James Corden: Stay strong Seamus Coleman. Every true football fan wishes you a strong recovery x