Everton 'leading race' to sign highly-rated defender linked with Celtic and Rangers
Celtic and Rangers have both been linked with the 17-year-old, who has caught the attention of numerous top clubs with his displays for the Cumbrian outfit.
Chelsea and Liverpool were both said to have been monitoring the situation while Carlisle are believed to have offered Branthwaite a new deal "some weeks ago", according to the News and Star newspaper.
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Hide AdLeicester were also understood to have been keeping tabs on Branthwaite, who has played 11 times for Carlisle in all competitions.
He is under contract at Brunton Park until the summer of 2021 but the League Two side are said to be expecting to sell him this month.