The 23-year-old is one of the most highly-sought after strikers in Europe, with 32 goals to his name already this term.
That followed on from his tally of 30 last term, and hosts of clubs are understood to be keen.
The Blues and United are reported to be leading the chase, but Suarez insists he is more than happy where he is.
The South American penned a new three-year deal in January this year, and he insists he would not have done so if he did not want to stay.
"I'm enjoying myself at Ajax," he told local Dutch television station AT5.
"I have not renewed my contract for nothing. I am here to stay."
Suarez is set to feature in this summer's World Cup finals, where he will look to form a potent strikeforce with Atletico Madrid's Diego Forlan.