Fulham have had a £20million bid rejected for Crystal Palace defender Joachim Andersen.
Palace value the 28-year-old Denmark international at £40m.
Fulham also had a bid rejected for Aston Villa centre back Diego Carlos, 31, last week but talks are continuing.
Meanwhile, Villa are keen on 24-year-old Feyenoord defender Lutsharel Geertruida, who can play at right back or as a central defender and has been capped 11 times by the Netherlands.
Fulham are also interested in Aston Villa defender Diego Carlos, pictured during pre-season
After finishing fourth in last season's Premier League, Villa have had a busy summer in the transfer market.
Ian Maatsen, Amadou Onana, Jaden Philogene, Ross Barkley, Enzo Barrenechea, Samuel Iling-Junior, Lewis Dobbin and Cameron Archer have all arrived at Villa Park as part of a summer spree costing more than £135m.
Villa have recouped a similar amount through player sales, with the likes of Moussa Diaby, Douglas Luiz and Omari Kellyman all moving on for significant fees.
Fulham have been much less active in the summer window so far.
Three players have joined the Cottagers, in Ryan Sessegnon, Emile Smith Rowe and Jorge Cuenca, while Joao Palhinha, Tim Ream and Kieron Bowie have departed.