No, and that information is not available to you through any official channel.
Inmates retain privacy rights over their communications, their contact lists, their commissary spending, and who sends them money or mail. That privacy exists on paper and in practice. The facility will not hand you a copy of his call list at the front desk or anywhere else. Visitation staff, counselors, and administrative personnel are not authorized to share that information with outside parties, including partners and spouses. The same applies to his approved visitor list, his mail records, and his account transactions.
The only person who can tell you who he is talking to is him. And whether he chooses to be transparent about that is itself information about the relationship.
This is one of the most common anxieties that comes with loving someone inside, and it makes sense that it surfaces. Incarceration removes your ability to observe the relationship the way you normally would. You cannot see who he spends time with, who he talks to, or what his daily life actually looks like. That uncertainty is real and it is uncomfortable.
But trying to access his private records is not the path through it. The path through it is a direct conversation about what you both expect from each other and whether those expectations are being honored. If the trust is not there, no call list is going to fix that. And if the trust is there, you do not need the list.
The question worth sitting with is what you would do with the information if you had it, and whether the answer to that question tells you something important about where things actually stand.