The former Sydney FC boss has just completed his first training camp in charge of the national team and has set aside the next few weeks to build strong relationships with the clubs of his Socceroos players.
Arnold will fly to Scotland on Wednesday to meet with Rodgers, with the progress of mercurial midfielders Daniel Arzani and Tom Rogic likely to be a key topic of conversation.
Joining Arnold on the worldwide charm offensive will be his Socceroos coaching assistant as they set out to lay the right foundations to avoid any potential conflicts between club and country.
"I feel one way to make life easier for the players and for ourselves is to make strong connections with the clubs in Europe," Arnold said.
"They own the players and we are borrowing them for a few days at a time. If we can make that work well then the relationship will make the players even better.
"Tomorrow I'm off to Scotland to visit Brendan Rodgers at Celtic, then Hearts, Hibs with Neil Lennon and then I'll shoot down to England."
The 55-year-old revealed he was looking forward to meeting Rodgers and was confident the former Liverpool coach was the right man to get the most out of Arzani.
"I do know Celtic rate him very, very highly," Arnold added.
"The kid has only been there two weeks and needs a little bit of time to settle.
"I’m sure the plans Celtic have will be great for him.”
