The Premier League club tabled an offer believed to be in the region of £8m for the Ghana international.
Swansea have turned down the approach having already rejected offers from West Ham United for goalkeeper Lukasz Fabianski and defender Alfie Mawson.
Ayew, 26, has scored 11 goals in 58 appearances for Swansea since joining from Aston Villa in January 2017.
It is also understood West Ham are still pursuing a deal for Fabianski. Talks between the clubs have continued but the Hammers are yet to increase their offer for the 33-year-old.
Manager Graham Potter has indicated he will have the final say on club transfer business following the Swans' relegation from the Premier League.
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