Cook, who was crowned young player of the year at Sunday's Football League awards, is out of contract at Elland Road next summer.
His is a situation similar to that of Sam Byram a year ago and the right-back eventually sealed a move to West Ham United with five months of his Whites deal remaining.
And Cook was unable to dispel fears that he could follow suit.
Asked about his future in West Yorkshire, the 19-year-old told the Yorkshire Evening Post: "Obviously I have still got a contract at Leeds and that’s all I can focus on.
"I enjoy playing my football here and the club is great and all the lads are great so why not?
"Every young footballer wants to end up in the Premiership - it’s being the right time and whether you are good enough.
"Everyone wants to be there at one point in their career.
"That would be the dream - to do it with Leeds."
York-born Cook, who's been at Leeds since the age of seven, broke into the first team a decade on and has played 81 times for the Whites in total, scoring twice.
In winning the Football League's young player of the year award, the England Under-19 international follows in the footsteps of illustrious duo Dele Alli and Gareth Bale, both of whom moved to Tottenham Hotspur, with the latter going on to cost Real Madrid a world-record fee.