According to sources close to the talks, new Inter manager Antonio Conte wants the 26-year-old out, while the board are also keen to sell the Argentina international.
The Nerazzurri are pushing Serie A champions Juve to consider a deal that would include Dybala, who saw his role reduced at the club following the arrival of Cristiano Ronaldo last summer.
Dybala, who had an impressive season in 2017-18 when he scored 22 league goals, has been moved into a deeper position to accommodate Ronaldo and managed just five goals in Serie A in the last campaign.
Juve are, however, reluctant to allow the 25-year-old to leave the club and they are yet to appoint a new head coach to replace Massimiliano Allegri, with Maurizio Sarri expected to be announced soon.
The Turin club do still retain an interest in Icardi, though, having tried to sign him last summer, before the move for Ronaldo had been confirmed.
Indeed, Juve sporting director Fabio Paratici has made contact with the player's wife and agent, Wanda Nara, over the possibility of getting a move over the line this time around.
Should a bid from abroad arrive, Icardi does still have a €110 million (£98m/$125m) release clause that only applies to clubs from outside of Serie A.
Icardi does, however, still want to stay at Inter, with Wanda Nara having revealed at the end of May that the player hoped to stay for "at least another year", with his contract not due to expire until 2021.
The former Sampdoria striker, who joined Inter in 2013, has not been far from controversy during his time at San Siro, with frequent reports of fallings out with team-mates, while he was stripped of the captaincy earlier in 2019.
In the aftermath of that decision he didn't play for the club for almost two months although, in spite of speculation that he would be moved on, he has consistently expressed his desire to stay.
Icardi, who has missed out on Argentina's Copa America squad, scored 17 goals in all competitions for Inter last season, with the Nerazzurri finishing fourth in the Serie A table to secure Champions League for the 2019-20 campaign.