Foxes chairman Milan Mandaric fired Allen last month just four games into his managerial reign.
However, Swindon have denied reports linking Sturrock with the post after claiming they have received no approach from the Foxes.
"Swindon Town would like to confirm that it has received no approach from any club with regard to manager Paul Sturrock," read a statement.
"The club would also like to confirm that any approach would not be welcome and the club remain committed to League One success under Paul Sturrock's guidance."
Sturrock led the Robins to promotion from League Two last season during his first year at the County Ground helm