King, 25, scored 16 Premier League goals for Bournemouth as they finished ninth, leading to claims that Tottenham were monitoring him.
"I was focusing on the season and finishing it strongly," King said when asked if he was aware of the speculation. "But I would be a liar if I said I hadn't noticed it. It was in most papers in England and you have got people tagging you and sending you links here and there.
"I was intrigued even being mentioned in the same sentence as Spurs, a big team who play in the Champions League.
"It is the summer holiday now and I've learned so much from the gaffer here.
"You never know in football but, hopefully, I will be here next year and I'm looking forward to working with the gaffer because he's been brilliant with me since the day I set foot on the training ground."
King signed a four-year contract with Bournemouth last summer and puts his goal scoring form down to the belief that manager Eddie Howe has shown in him since his arrival from Blackburn in 2015.
"I'm a different player in that I'm fitter and have maybe got my hunger back," he said. "The gaffer bought me for a reason -- he saw the potential and talent I had. At Blackburn, I was playing out of position, as I was when I came here as well, but now I've got a position I'm used to playing and the position I want to play."
The former Manchester United player now wants to help Bournemouth to progress further and improve his own goals tally.
"I'm very proud to say I played in a team which finished ninth in the Prem," he said. "If you look at the teams who finished above us, most of them were fighting for the top four.
"I think the team was brilliant. We managed to come back after we struggled for form. I think we progressed from last season and, hopefully, next season we can progress even more. I want to help this team climb higher and want to improve my goals and assists, and try to better myself next season."