The midfielder, 24, is generating interest from several clubs in England - Swansea City and Watford also said to be interested.
"There's been interest in Craig from a number of clubs outside Scotland," his agent Gerry Carlile Carlile told the Press Association.
"Craig is under contract at Rugby Park and until such time that a club agrees terms with Killie, then he will remain a Kilmarnock player and that's where he will concentrate all his energy and attention."
Bryson made his senior Scotland debut in November, coming off the bench against the Faroe Islands.
The link with Bryson follows suggestions that the Iron midfielder Josh Wright is wanted by Championship rivals Reading.