"It is not done yet, but it is close to being done,'' Clement told reporters on Tuesday.
Included in the impending move is Wales defender Neil Taylor, who would be moving in the opposite direction – from Swansea to Aston Villa, who will receive a fee up to £5 million, according to reports.
This is not the first time Swansea are attempting to recruit Ayew. Last season, the 25-year-old almost reunited with his elder brother, Andre, at the Liberty Stadium. Andre later joined West Ham.
"Ayew can play wide or through the middle and I like that versatility." Clement said.
Ayew is currently representing Ghana at the Africa Cup of Nations in Gabon. The Black Stars have reached the semi-final stage, with Ayew likely to feature against Cameroon on Thursday.
However, his absence would not delay the Swansea move, since the player recently completed a medical with the Football Association for insurance purposes.