The Blues will fork out £12m in their bid to land the Ghana international from their Premier League rivals.
Manager Antonio Conte has identified Ayew as the player needed to solve a problem the Italian has identified in the midfield.
A media report in the UK claims Chelsea will make £12m available in their bid to capture the talented player from the Welsh.
However, a source close to the player has told Ghana's leading football news outfit, ghanasoccernet.com that the Welsh side will demand at least £30m for Ayew.
Swansea are aware that they would be unable to keep the Ghana star as interest in the midfielder soars following his impressive first season in the English Premier League.
Sunderland is seeking a deal for the Swansea star while Liverpool is also linked to the son of Ghana legend Abedi Pele.
Ayew is set to leave the Liberty Stadium this summer as interest will surely grow in the midfielder.
However, the Swans will seek to exact maximum profit from the sale of the player they acquired on a free transfer last season.
He will become the second player Conte has signed after Ngolo Kante clinched the move from Leicester City on Saturday.