Koeman shared a picture on his Twitter profile of Coleman on crutches and wearing a protective boot along with the caption: “Today we visit Seamus Coleman and his family! Looking strong and positive.”
Coleman suffered a horrific double leg break while on international duty with Ireland, when he was challenged by Wales defender Neil Taylor in a World Cup qualification match.
The 28-year-old underwent surgery two and a half weeks ago and is now recuperating in his home town of Killybegs in County Donegal, where he was visited by Koeman and Jagielka, as well as fitness coach Jan Kluitenberg and head of medical services Matt Connery.
Koeman told evertonfc.com: "We made the visit to show our support for Seamus, the support of his team-mates and the support he has from all Evertonians. Every player in these circumstances needs this level of support to recover well.
“Seamus is positive and he is feeling strong. He is really grateful for all of the messages he has received from Everton fans and from people all over the world.
“Before he comes back (to Everton) to start his rehabilitation, he will spend up to 10 more days at home in Killybegs before starting out on his recovery from the injury.”
Everton revealed on their website that the club received almost 2,000 emails of support in the wake of Coleman’s injury, from as countries as far afield as Finland, Egypt, Bangladesh, Colombia and New Zealand.
The club also said they received dozens of letters and cards, with Koeman and Jagielka taking a selection of them to Ireland to give to Coleman.
Today we visit Seamus Coleman and his Family! Looking strong and positive pic.twitter.com/T0bSx5yCoI
— Ronald Koeman (@RonaldKoeman) April 11, 2017
"We had a really good chat with Seamus and it was great to see him in such good spirits,” Jagielka added.
“He was smiling and feeling positive, which is all we can ask for. He knows we are all here to help him along the way.”
Coleman will be side-lined until next season but could be back running by August if his recovery goes to plan.