The full-back had surgery two and a half weeks ago on the horrific double leg break he suffered on international duty with the Republic.
Coleman is spending his initial period of recovery in his home town of Killybegs in County Donegal, and was visited on Tuesday by Koeman, Jagielka, 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."
Read the full article on eurosport.co.uk: Koeman and Jagielka among Everton party to visit stricken Coleman in Ireland