The 25-year-old midfielder has his contract with Porto running out in the summer and is said to have decided against extending his deal with the club.
Many clubs, including Premier League giants Arsenal, have been put on alert after Otavio rejected the chance to sign a new deal with the Portuguese outfit.
According to Italian outlet Tutto Mercato, Leicester are one of the clubs interested in acquiring the services of the midfielder.
Apart from the Foxes, Italian Serie A clubs Roma, Juventus, Napoli and AC Milan are also keen on signing the Brazilian, whose time at Porto is nearing an end.
Leicester, Roma, Juventus, Napoli and AC Milan are claimed to have made offers to Otavio.
However, Roma are leading the race to snap him up, while AC Milan technical director Paolo Maldini has talked to the player over the phone.
With a host of clubs interested in signing Otavio, it remains to be seen if Leicester can convince the midfielder to move to the King Power Stadium.