Ayew, 26, was the Swans' top scorer with 11 goals as they were relegated from the Premier League last season.
The Ghanaian has been linked with Crystal Palace and Fulham but the Welsh club have yet to receive a bid that matches their valuation.
"There's no further news on Jordan - he's just not been here," Swansea boss Graham Potter told BBC Sport Wales.
"That tells you that he's not part of what we're trying to do, by his own actions.
"It's whether we can get a good enough deal for the club. Otherwise, that's going to be an interesting time for him."
Ayew joined Swansea from Aston Villa in 2017 and, after a slow start at the Liberty Stadium, established himself in the first team last season.
Newly promoted Premier League side Fulham had an offer of £8m rejected for him in June, and it is thought the Swans value him at around twice that figure.
They are also looking to offload midfielder Sam Clucas, whose £8m move to Burnley collapsed after they failed to agree personal terms.
If Clucas leaves, Swansea hope to sign Brentford midfielder Ryan Woods in a transfer which would be worth between £6m and £7m.
Potter admits he must sell players in order to make such signings before the transfer window shuts on Thursday.
"There's an element of that. We need to be careful with what we're doing," he added.
Jordan Ayew refuses to train over move speculation
08 August 2018
Jordan Ayew is moving closer to leaving Swansea City after refusing to train with the Championship team.