Flamengo have turned down Fulham’s initial £21million offer for Pedro but are braced for further bids.
The 26-year-old wants to move to the Premier League but Fulham face competition from Benfica and Zenit St Petersburg.
Fulham manager Marco Silva is also looking at Zapata as a potential Mitrovic replacement after the Cottagers sold the Serb to Saudi side Al-Hilal for £46m.
Atalanta want to keep Zapata despite signing Gianluca Scamacca from West Ham.
Fulham have also sounded out Arsenal forward Folarin Balogun, who is now expected to join Monaco, while Silva has denied interest in Juventus striker Moise Kean.
Silva wants three strikers in his squad, with Raul Jimenez set to start away at Arsenal tomorrow and Carlos Vinicius likely to deputise from the bench.
Fulham are also chasing two full-backs, with Leicester City’s Timothy Castagne their primary target.
AC Milan’s Fode Ballo-Toure, Union Berlin’s Josip Juranovic, Southampton’s Kyle Walker-Peters and Rennes’s Arthur Theate are also being considered.