The 34-year-old is set to leave Sunderland after the Black Cats were relegated from the Premier League.
Defoe – who will be part of England’s attack against Scotland in Saturday’s World Cup qualifier at Hampden Park – had a spell at Bournemouth earlier in his career, and is reported to have agreed a three-year deal at the Vitality Stadium, worth £60,000 per week.
“What I want to do is get my head down and focus on England, the two games, and then after that everyone will know,” Defoe said on Sky Sports News HQ.
“It’s documented about the Bournemouth thing. It’s a club close to my heart anyway, for obvious reasons. I was there as a kid. I think I was 18, on loan from West Ham.
“It’s a special place, with a top manager, and a team that’s done so well from where they’ve come from. A unique story.”
Defoe is said to have been able to leave Sunderland on a free transfer because of a clause in his contract regarding relegation.
Speaking to BBC Radio 5Live, Defoe added: “It’s out there, a lot of people obviously knew, I did a medical and said when this is finished and I’ve had a break, come July everyone will know anyway.
“Two and a bit years at Sunderland, I enjoyed my time there, it’s not nice when you get relegated, I don’t think it’s fair on the Sunderland fans to come out so soon after they’ve been relegated and say ‘yeah, I’m signing for someone else’.
“It’s too soon to put it out there. At the right time, I would like to say ‘this is the club I’ll be playing for’.”
Before heading back to the south coast for the start of pre-season training, Defoe, who scored 15 goals for Sunderland last season, will be involved for England, who also play France on June 13 following their showdown against Scotland.
England manager Gareth Southgate arranged a top-secret trip to the Royal Marines’ Commando Training Centre in Devon as part of the build-up to the Scotland game.
Defoe, who returned to England following a spell at Toronto FC, feels the experience was worthwhile, if unexpected.
He said on BBC Radio 5Live: “When the Marines walked into the room, I was like ‘woah, what is going on here?’ It was ‘right, get up we are going on the coach down south’ and that was it.
“It was just the unknown, we didn’t know what was coming, but I was just really excited to be honest.
“You know when you don’t know what is coming, it is just like ‘let’s see’.
“We knew it would be a test and that, but the whole experience was amazing, it was just so good.”