The U's will conduct individual fitness tests in Essex on Friday before the squad join together to make the short trip to Ireland on Monday for the start of their summer preparations.
Dunne will also use the opportunity to strengthen links with numerous contacts in his native homeland, including coaches and scouts, boosting Colchester's chances of attracting promising talent.
"Going over will give us the chance to have the squad in a closed environment, where we can concentrate fully on what we have to do without any distractions," he told the club's official website.
"The lads will be together all the time as well, giving them the chance to bond again after a summer away from each other."
Dunne added: "I enjoyed a very successful trip there last season where I met representatives from the Irish FA and the Irish PFA, and this trip gives me the chance to further cement those relationships.
"Over the years, plenty of lads from Ireland have made the grade in all the English leagues and we want to be at the front of the queue as a destination for the best players, both now and into the future."