The Marseille winger is keen to complete a move away from L’OM with the Premier League his preferred transfer destination.
Harry Redknapp is desperate to add some quality to his Rangers squad, with the London club gearing up for another relegation battle.
Swansea boss Garry Monk, meanwhile, has identified Ayew as the ideal addition to his group, with the Welsh club keen to build on the positive start they have enjoyed in the Premier League, having won three games from three so far.
The mood around QPR, meanwhile, has been lifted after the club recorded their first win of the season at home to Sunderland.
Redknapp is still eager to complete a deal for Ayew following the departure of Loic Remy to Chelsea.
Valued at around £10 million, a transfer tug-of-war could ensue in the next 24 hours, with Swansea unlikely to give up easily.
Ayew was one of the few shining lights for Ghana at the World Cup in Brazil, scoring well-taken goals against the USA and Germany during the group phase.
Check out Ayew scoring a hat-trick for Marseille last term. Who would he better suit - QPR or Swansea?