Bjarnason was used as a late sub for Villa against Hull.
Iceland international Bjarnason, who played at the World Cup with Iceland, has endured a difficult spell with Villa since his move to the club from FC Basel in January 2017.
He enjoyed an eventual breakthrough into the first team towards the end of last season, shining under Steve Bruce after featuring just seven times before the turn of the year in the Championship.
He remains a crucial part of Bruce's plans, coming off the bench to feature for seven minutes during Villa's opening-day win over Hull City. But the signing of John McGinn from Hibernian may push the 70-cap down the pecking order.
Villa boast a whole list of central midfield talent, including the likes of Conor Hourihane, Mile Jedinak, Glenn Whelan and Henri Lansbury at Villa Park. With McGinn added to that list, a sale could occur.
That could see Empoli find success in talks to land the versatile midfielder, who are under no pressure to complete a deal for Bjarnason today with the European transfer window closing as normal on August 31.