The Leicester Mercury says captain Morgan is close to agreeing a contract extension with the club.
Morgan's representatives have been in discussions with City and it is understood talks have been productive.
The final details of the contract extension are being finalised and, although the actual terms are not known, it means Morgan will remain with City beyond this coming season.
Morgan was due to be out of contract this summer. However, City activated a clause in his contract to take up their option of another year.
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