The 38-year-old appeared to announce his Millwall exit on social media during the week, after his half-season stint with the club.

Cahill managed 10 appearances off the bench for Millwall after joining his original English club in late January, with minimal impact.

The move had been engineered with a view to facilitating Cahill's hopes of being part of Australia's 2018 World Cup squad, but Harris didn't rule out re-signing the Australian for next season.

"We've left it open," Harris told the club website.

"Do I expect to see Tim Cahill come back and play for us next year? I'll be surprised, I've got to be honest but I would never rule anything out.

"Our relationship is really strong, I've loved having him here. Will he be back in the future working? That's a possibility as well.

"What I do know with Tim is that he is in great physical condition - top, top shape. He's an excellent character in the dressing room and has a lot to offer in football around the world.

"Whether he wants to go and play 90 minutes every week or whether he wants to be part of a group where he can have an input as an impact sub or in the dressing room then he'll have a lot to offer at various clubs around the world as well.

"It's an ongoing conversation, but probably not one that's going to take place between me and Timmy until well after the World Cup."

He added: "How we've left it is that he's got a World Cup to hopefully go and prepare for and then he's got to think about what the bigger picture holds for him.

"What we have to remember is that his family are from Australia, live in New York and he's in London. That's not an easy relationship to have."

Harris added a ringing endorsement for Cahill, insisting Bert van Marwijk should take the veteran as part of his final 23-man Socceroos 2018 World Cup squad.

"Is he going to get to the World Cup? Time will tell," he said.

"If I was the Australian manager, he'd be the first name in the squad list because of what he brings off the pitch as well as on it."