Swansea hope to seal a £18million deal for Andre Ayew’s return.
West Ham have rejected a £15m offer for the Ghana striker they paid £20.5m for.
But the Swans will go back with their improved offer before the transfer window closes on Wednesday.
David Moyes wants to make sure he has enough cover in attack before allowing Ayew, 28, to leave.
Andy Carroll is out with a foot injury, while out-of-favour Javier Hernandez is wanted by Turkish side Besiktas.
West Ham have told Fulham they will go to £20m to snare midfielder Tom Cairney — after a £15m bid was rejected.
Meanwhile, Swansea could yet make an approach for Atletico Madrid winger Nico Gaitan.