The two clubs have been locked in talks for months over a fee for the England international, who was outstanding on-loan for Roma last season.
Fonseca has made it clear to his board that Smalling must be a priority, despite the arrival of Marash Kumbulla from Hellas Verona.
However, Corriere dello Sport says there remains a huge difference in valuations between the two clubs.
Last week, Fonseca said: "I am confident, we are working to have Chris in the squad.
"I am in contact with him, I spoke to him also yesterday. He wants to go back to Roma and we want to have him back with us.
"In the next few days I think we can have him back here with us."