The in-demand striker was the subject of a bid from Brighton in January when they met his release clause of £1.1million - but the Cherries persuaded him to stay with a new long-term deal.
However, Sky Sports revealed last week that Grabban's new deal also has a clause - which is around £3million.
Now the likes of his former club Crystal Palace, Cardiff City and Middlesbrough are all believed to be looking to land him, having seen him hit 22 goals this term.
"The thing with speculation is you never know if it is true or not. If teams from the Premier League are interested in me then that is flattering," he told the Daily Echo.
"As a player, it is a compliment to be linked with other clubs.
"Everyone has ambitions to play in the Premier League, I think it is the same for every footballer but at the moment they are just rumours."
Should he remain at Bournemouth, then Grabban is confident they can compete with the bigger clubs.
"People might look at where we have come from and the stadium and see us as a small club but we have a wealthy owner so it doesn't look like we need to sell players," he said.
"We have proved that by rewarding people when they have done well so I don't think any interest is a worry to the club.
"Outsiders might look and end up underestimating us and there's nothing wrong with that, you just go out there, try to excel and prove those people wrong.
"I think we have proved we are more than capable of beating the best sides in this division and we are looking at getting into the play-offs as a minimum target for next season.
"We had a hiccup and that was the only reason we missed out this time. We already have a great squad at Bournemouth and with a few more additions we can definitely push for promotion and progress the club.
"The dream would be to keep all the players and while these things don't always happen, hopefully we can keep this squad together because we have something special building."