Vardy, 38, is a free agent after coming off contract at Leicester over the summer.
The veteran striker is interesting West Ham and Brentford, while he is also keen to hear from his former Leicester manager Brendan Rogers at Celtic.
However, the Daily Mail says Napoli are now entering the fray.
A serious injury for Romelu Lukaku suffered over the weekend has Napoli eyeing Vardy as a stop-gap addition. It's been suggestion Lukaku may need thigh surgery which will leave sidelined for months.
As such, Azzurri chief Giovanni Manna is considering a move for free agent Vardy this week.
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Vardy