The 37-year-old is a free agent after leaving Stoke City and has been linked with a deal at West Ham United already this summer.
Burton are hopeful, however, that the prospect of continuing his career without having to move from his Derbyshire base will appeal.
“I’ve had a few offers but none really viable, thinking about my family,” said Delap.
Burton also fielded former Northampton goalkeeper Chris Dunn against Ilkeston as he looks for a move away from Town's new lodgers Coventry City.
Source: Cobblers Mad