Arsenal have been open to offers for Partey over the course of the transfer window despite Mikel Arteta insisting that he is a key part of his plans.
The midfielder has attracted interest from several clubs in Europe and has also been linked with a move to Saudi Arabia.
Juventus are amongst the clubs who lodged enquiries for the Ghana midfielder earlier in the transfer window.
There are suggestions that with the Serie A giants missing out on signing Franck Kessie, they could make a move for Partey but according to Italian outlet TuttoJuve, it is unlikely to happen.
Allegri likes the Arsenal midfielder and would want him in his side but the costs of doing a deal are prohibitive for Juventus.
Partey is on big wages at Arsenal and Juventus are not in a position to take on that salary, especially with no European football next season.
Arsenal are likely to demand more than €20m for the midfielder and Juventus also cannot afford that level of fee at the moment.
