Alessandro Matri and Fabio Quagliarella are considering improved offers from Everton and Norwich respectively.
The Juventus strikers are pushed even more to the sidelines this season with the arrival of Carlos Tevez and Fernando Llorente.
The Premier League beckons for the two Italian forwards, as previous bids are reportedly raised over the weekend.
Everton are renewing their attempts to sign Matri, who was also of interest to Milan and Napoli, with an improved offer worth €12m (£10.4m).
The Rossoneri in particular could make a new offer for Matri after learning of Robinho’s thigh injury.
As for Quagliarella, he turned down a previous proposal from Norwich, but the Canaries are not giving up.
West Ham United are also thought to be tracking €10m-rated (£8.6m) Quagliagol.