Vardy, 38, is a free agent after he decreased in Leicester in the summer in Leicester.
The veteran striker is interesting West Ham and Brentford, while he also likes to hear from his former Leicester manager Brendan Rogers at Celtic.
The Daily Mail, however, says that Napoli is now entering the fight.
A serious injury for Romelu Lukaku has the weekend since Napoli sees Vardy as a stop-gap addiction. It has been a suggestion that Lukaku may need dij surgery that remains offside for months.
As such, Azzurri chef Giovanni Manna is considering a step for free agent Vardy this week.