Bournemouth have been tracking Cook for the majority of the January transfer window, but the midfielder has reportedly told them that he does not want to leave Elland Road.
Cook is loving his time with Leeds and he has no intention to leave in the imminent future.
The 18-year-old feels that he is progressing well at a club where he is playing regularly.
Cook sees his short-term future at Leeds, and does not want to unsettle himself by moving in mid-season, unless Cellino accepts an offer.
Steve Evans has consistently said that Leeds will not listen to bids for Cook, who is arguably their most promising youngster.
Leeds are set to lose Sam Byram, however, with the defender likely to move to Everton in the coming days.