The Ghana international, whose contract with Juve runs out at the end of the season, is rumoured to have agreed terms with the Black and Blues, amid links to AS Roma and Turkish sides Fenerbahce and Galatasaray.
Speculations say the Old Lady are also trying to convince the 29-year-old for a contract extension, but his limited opportunities at the Allianz Stadium have turned his heart away.
“The transfer market is made up of certain dates, but we are working everyday and tracking various situations," Ausilio responded when asked about the reported summer arrival of Asamoah and Lazio defender Stefan de Vrij, according to Football Italia.
"We want to ensure that we are ready when called upon and we’ll see if we’ve managed to do something when the time comes.
“We are working, but so is every other club that wants to improve from season to season.”
His injury troubles, partly to blame for his bit-part role, Asamoah has made 52 league outings in all since summer 2014, having transferred from Udinese in 2012.
He has 16 Serie A appearances, involving 15 starts, to his name so far, this season.
Five Serie A titles, three Coppa Italia winner's medals and three Super Cup golds make up his trophy haul.