However, the 27-year-old has so far refused to accept a move away from the club - which in turn forced the sale of Anthony Martial to Monaco over the weekend.
To report a balanced financial set of results for the year, Lyon had to sell by the weekend and with Gomis hesitating they had to look elsewhere for money, and Monaco came in for the highly-rated Martial.
Aulas says that Swansea have already agreed terms for the French international striker.
"I had the feeling and I was even almost sure we could have convinced Bafe [to leave]," Aulas told L'Equipe.
"The Swansea chairman came to Lyon to sign the commitment and we checked the offer was superior to what Bafe earns at Lyon."
Aulas insists that they are looking to sort out Gomis' future, but it is down to the player's behaviour.
"It has become a behaviour problem more than a sporting problem. I could not imagine he would go against his own interests."