Pjanic left for Barcelona last year in a swap deal with Arthur, but his time in Spain has been unhappy, the midfielder starting just six LaLiga games under Ronald Koeman in 2020-2021.
There is speculation the 31-year-old wants to move back to Turin, where he could reunite with Allegri, the coach under whom he won six trophies in Italy.
Allegri, though, appears more interested in transforming Ramsey into a defensive midfielder ahead of the start of 2021-2022.
The Wales international started at the base of a midfield three in Sunday's (AEST) 2-1 friendly win over Monza, regaining possession four times and completing 100 per cent of his passes in his 45-minute outing.
Ramsey has been linked with a possible return to the Premier League but it appears Allegri has important plans for the 30-year-old if he is prepared to embrace the change in position.
"The club handles the transfer market. We speak every day," Allegri said.
"The squad... it's a good squad. Ramsey played very well in front of the defence today and I think Aaron, in front of the defence, can become a really important player.
"[Pjanic] gave me some great victories. He's a Barcelona player, though.
"We have talented players and I think, if Ramsey is convinced to play in front of the defence, he can become important. He runs less there and can rest more on the ball."
Juve plays Barca in the pre-season Joan Gamper Trophy match on 9 August.