The Toffees are in a horrible run of form, kept out of bottom place in the Premier League standings only due to goal difference.
They want to improve by making additions in the transfer window and one of the positions they want to fill up this month is striker.
Everton are interested in Atalanta star Duvan Zapata, but look set to be unable to sign him on loan.
The Toffees are keeping their eye on Serie A though and have now identified Arnautovic as a target, according to Italian outlet Tutto Mercato.
Everton have already established communication through agents as they explore a deal to bring the former West Ham United star to Goodison Park.
Another Serie A striker of interest to Everton is Udinese star Beto, but for him an offer is claimed to have been refused by the Italians.
Arnautovic was of interest to Manchester United last summer but that transfer fell through and it remains to be seen if he makes his way back to the Premier League with Everton.
