The 23-year-old has established himself as one of the finest full-backs operating outside the Premier League since moving to Portman Road from Tranmere Rovers in 2011.
Speculation suggesting he will soon be mixing it with the top flight elite refuses to go away, with Cresswell reported to have attracted plenty of admiring glances over the summer.
He has, however, remained on the books at Ipswich and claims he has no intention of moving on any time soon - with move rumours likely to resurface in January.
Cresswell told the Green Un: "It's nice to hear that people might be interested, but I just get my head down and play my football.
"My agent and others deal with and talk about that, but I honestly didn't hear a thing at all (over the summer).
"There's not a player out there that wouldn't want to play in the Premier League - that's the same for me and every player at Ipswich. I love it down here, though, and I just have to keep working hard.
"Everyone, even the best in the world, Messi and Ronaldo, will always be looking to make improvements. Working under the gaffer (Mick McCarthy) and TC (Terry Connor), I think I'm at the right place to progress as a player.
"I'm 23 years old, I'm still young and I've hopefully got at least 10 more years in the game.
"Getting promotion with Ipswich would be the perfect ambition for me to achieve. That would be killing two birds with one stone. And who is to say we can't achieve it next season or even this one?"