The Foxes are very eager to add the center-back to their squad, as they seek to improve manager Brendan Rodgers' defense.
However, Leicestershire Live states that Chelsea must decide if they will keep, loan, or sell Colwill this summer.
The 19-year-old was impressive at Huddersfield on loan in the Championship last term.
Transfer expert Fabrizio Romano states that Chelsea have not made up their mind on Colwill.
His future may depend on how many center-backs Chelsea sign this summer.