The talented 24-year-old is considered to be among the best left-backs currently plying their trade outside of the Premier League, and has been billed as such by boss Mick McCarthy.
His obvious ability has not gone unnoticed within the top-flight ranks and speculation regarding a step up in class has been building steadily over recent years.
Cresswell has, however, penned a contract through to 2017 at Portman Road and has no intention of breaking that agreement.
He believes he is capable of gracing the top level with Ipswich and will continue to ignore the endless rounds of transfer gossip until something of substance is put to him.
He said in the Green Un: "I just get on with my football.
"Whatever gets said is out of my hands, but I'm happy down in Ipswich and that's why I've signed a new deal. I love it down here.
"As I've said before, every player wants to play at the highest level. To get there with Ipswich would kill two birds with one stone.
"We're in the top six now and we want to stay there."
Arry has got to be the most overrated english manager of the last 20 years i hate the guy- realbarneycarey